RD Sharma Class 10 Solutions Chapter 3 Exercise 3.2 (Updated for 2021-22)

RD Sharma Class 10 Solutions Chapter 3 Exercise 3.2

RD Sharma Class 10 Solutions Chapter 3 Exercise 3.2: This exercise evaluates your understanding of how to generate graphs of linear equations while solving systems of simultaneous linear equations in two variables. Experts at Kopykitab provide all of the RD Sharma Class 10 Solutions by connecting students at various levels. For any reference relating to the exercise questions, the RD Sharma Solutions for Class 10 Maths Chapter 3 Exercise 3.2 PDF is provided here.

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RD Sharma Class 10 Solutions Chapter 3 Exercise 3.2

Access answers to RD Sharma Solutions Class 10 Maths Chapter 3 Exercise 3.2- Important Question with Answers

Solve the following systems of equations graphically :
Question 1.
x + y = 3
2x + 5y = 12 (C.B.S.E. 1997)
Solution:
x + y = 3
=> x = 3 – y
Substituting some different values of y, we get the corresponding values of x as shown below
RD Sharma Class 10 Solutions Pdf Free Download Chapter 3 Pair Of Linear Equations In Two Variables
Now plot the points on the graph and join them 2x + 5y = 12
2x = 12 – 5y
⇒ x = 125y2
Substituting some different values of y, we get the corresponding values of x as shown below
Class 10 RD Sharma Pdf Chapter 3 Pair Of Linear Equations In Two Variables
Now plot the points on the graph and join them we see that these two lines intersect each other at (1, 2)
x = 1, y = 2
Answers Of RD Sharma Class 10 Chapter 3 Pair Of Linear Equations In Two Variables

Question 2.
x – 2y = 5
2x + 3y = 10 (C.B.S.E. 1997)
Solution:
x – 2y = 5 => x = 5 + 2y
Substituting some different values of y, we get the corresponding values of x as shown below
RD Sharma Mathematics Class 10 Pdf Download Free Chapter 3 Pair Of Linear Equations In Two Variables
Now plot the points are the graph and join them
2x + 3y = 10 => 2x = 10 – 3y
⇒ x = 103y2
Substituting some different values of y We get the corresponding values of x as shown below :
RD Sharma Class 10 Maths Chapter 3 Pair Of Linear Equations In Two Variables
Now plot the points on the graph and join them we see that these two lines intersect each other at (5, 0)
x = 5, y = 0
RD Sharma Maths Book For Class 10 Solution Chapter 3 Pair Of Linear Equations In Two Variables

Question 3.
3x + y + 1 = 0
2x – 3y + 8 = 0 (C.B.S.E. 1996)
Solution:
3x + y + 1 = 0
y = -3x – 1
Substituting the values of x, we get the corresponding values of y, as shown below
RD Sharma 10 Solutions Chapter 3 Pair Of Linear Equations In Two Variables
Now plot the points on the graph and join them
2x – 3y + 8 = 0
⇒ 2x = 3y – 8
⇒ x = 3y82
Substituting some different values of y, we get the corresponding values of x as shown below
Solution Of RD Sharma Class 10 Chapter 3 Pair Of Linear Equations In Two Variables
Now plot the points on the graph and join then we see that these two lines intersect, each other at (-1, -2)
x = -1, y = 2
RD Sharma Class 10 Book Pdf Chapter 3 Pair Of Linear Equations In Two Variables

Question 4.
2x + y – 3 = 0
2x – 3y – 7 = 0 (C.B.S.E. 1996)
Solution:
2x + y – 3 = 0 => y = -2x + 3
Substituting some different values of x, we get the corresponding values of y as shown below:
RD Sharma 10 Chapter 3 Pair Of Linear Equations In Two Variables
Now plot the points and join them 2x – 3y – 7 = 0
2x = 3y +7
x = 3y+72
Substituting some different values of y, we get corresponding values of x as shown below:
10th Maths Solution Book Pdf Chapter 3 Pair Of Linear Equations In Two Variables
Now plot the points on the graph and join them we see that these two lines intersect each other at (2, -1)
Maths RD Sharma Class 10 Solutions Chapter 3 Pair Of Linear Equations In Two Variables

Question 5.
x + y = 6
x – y = 2 (C.B.S.E. 1994)
Solution:
x + y = 6 => x = 6 – y
Substituting some different values of y, we get the corresponding values of x as shown under
RD Sharma Class 10 Textbook PDF Chapter 3 Pair Of Linear Equations In Two Variables
Now plot the points on the graph and join them
x – y = 2 ⇒ x = 2 + y
Substituting some different values of y, we get the corresponding values of x as shown below:
RD Sharma 10 Class Solutions Chapter 3 Pair Of Linear Equations In Two Variables
Now plot the points on the graph and join them
We see that there two lines intersect each other at (4, 2)
x = 4, y = 2
RD Sharma Maths Class 10 Solutions Chapter 3 Pair Of Linear Equations In Two Variables

Question 6.
x – 2y = 6
3x – 6y = 0 (C.B.S.E. 1995)
Solution:
x – 2y = 6
x = 6 + 2 y
Substituting some different values ofy, we get the corresponding values of x as shown below:
Class 10 RD Sharma Chapter 3 Pair Of Linear Equations In Two Variables
Now plot the points and join them
3x – 6y = 0 ⇒ 3x = 6y ⇒ x = 2y
Substituting some different values of y, we get corresponding the values of x as shown below:
RD Sharma Class 10 Book Pdf Free Download Chapter 3 Pair Of Linear Equations In Two Variables
plot the points on the graph and join them We see that these two lines intersect each other at no point
The lines are parallel
There is no solution
RD Sharma Maths Class 10 Solutions Pdf Free Download Chapter 3 Pair Of Linear Equations In Two Variables

Question 7.
x + y = 4
2x – 3y = 3 (C.B.S.E. 1995)
Solution:
x + y = 4 => y = 4 – x
Substituting some different values of y, we get the corresponding values of x as shown below:
RD Sharma Class 10 Pdf Ebook Chapter 3 Pair Of Linear Equations In Two Variables
Now plot the points and join them 2x – 3y = 3
⇒ 2x = 3 + 3y
⇒ x = 3+3y2
Substituting some different values of y, we get the corresponding values of x as shown below:
RD Sharma Class 10 Solution Chapter 3 Pair Of Linear Equations In Two Variables
Now plot the points on the graph and join them we see that these two lines intersect each other at (3, 1)
x = 3, y = 1
RD Sharma Class 10 Pdf Free Download Full Book Chapter 3 Pair Of Linear Equations In Two Variables

Question 8.
2x + 3y= 4
x – y + 3 = 0 (C.B.S.E. 1995)
Solution:
2x + 3y = 4
=> 2x = 4 – 3y
=> x = 43y2
Substituting some different values of y, we get corresponding values of x as shown below:
Class 10 RD Sharma Solutions Chapter 3 Pair Of Linear Equations In Two Variables
Now plot the points are the graph and join them
x – y + 3 = 0
x = y – 3
Substituting some different values of y, we get corresponding values of x as shown below:
Learncbse.In Class 10 Chapter 3 Pair Of Linear Equations In Two Variables
Now plot the points on the graph and join them
We see that these two lines intersect each other at (-1, 2)
x = -1, y = 2
RD Sharma Solutions Class 10 Chapter 3 Pair Of Linear Equations In Two Variables

Question 9.
2x – 3y + 13 =0
3x – 2y + 12 = 0 (C.B.S.E. 2001C)
Solution:
2x – 3y + 13 = 0
2x = 3y – 13
=> x = 3y132
Substituting some different values of y, we get corresponding values of x as shown below
RD Sharma Class 10 Pdf Chapter 3 Pair Of Linear Equations In Two Variables
Plot the points on the graph and join them 3x – 2y + 12 = 0
3x = 2y – 12
x = 2y123
Substituting some different values of y, we get corresponding values of x as shown below
RD Sharma Class 10 Solutions Chapter 3 Pair Of Linear Equations In Two Variables
Plot the points and join them We see that these two lines intersect each other at (-2, 3)
x = -2, y = 3
RD Sharma Class 10 Solutions Pair Of Linear Equations In Two Variables

Question 10.
2x + 3y + 5 = 0
3x – 2y – 12 = 0 (C.B.S.E. 2001 C)
Solution:
2x + 3y + 5 = 0
2x = – 3y – 5
x = 3y52
Substituting some different values of y, we get corresponding values of x as shown below
Pair Of Linear Equations In Two Variables Class 10 RD Sharma
Now plot the points on the graph and join them
3x – 2y – 12 = 0
3x = 2y +12
x = 2y+123
Substituting some different values of y, we get corresponding values of x as shown below:
RD Sharma Class 10 Chapter 3 Pair Of Linear Equations In Two Variables
Now plot the points on the graph and join them we see that these lines intersect each other at (2, -3)
x = 2, y = -3
RD Sharma Class 10 Solutions Pdf Free Download Chapter 3 Pair Of Linear Equations In Two Variables
Show graphically that each one of the following systems of equations has infinitely many solutions :

Question 11.
2x + 3y = 6
4x + 6y = 12 [CBSE2010]
Solution:
2x + 3y = 6 ……….(i)
4x + 6y = 12 ……….(ii)
2x = 6 – 3y
Class 10 RD Sharma Pdf Chapter 3 Pair Of Linear Equations In Two Variables
Now plot the points of both lines on the graph and join them, we see that all the points lie on the same straight line
This system has infinitely many solutions
Answers Of RD Sharma Class 10 Chapter 3 Pair Of Linear Equations In Two Variables

Question 12.
x – 2y = 5
3x – 6y = 15
Solution:
x – 2y = 5
x = 5 + 2y
Substituting some different values of y, we get corresponding values of x as shown below:
RD Sharma Mathematics Class 10 Pdf Download Free Chapter 3 Pair Of Linear Equations In Two Variables
Now plot these points on the graph and join them
3x – 6y = 15
=> 3x = 15 + 6y
x = 15+6y3
Substituting some different values of y, we get corresponding values of x as shown below:
RD Sharma Class 10 Maths Chapter 3 Pair Of Linear Equations In Two Variables
Now plot there points on the graph and join then
We see that these two lines coincide with each other
This system has infinitely many solutions.
RD Sharma Maths Book For Class 10 Solution Chapter 3 Pair Of Linear Equations In Two Variables

Question 13.
3x +y = 8
6x + 2y = 16
Solution:
3x + y = 8 => y = 8 – 3x
Substituting some different values of x, we get corresponding values of y as shown below:
RD Sharma 10 Solutions Chapter 3 Pair Of Linear Equations In Two Variables
Now plot these points on the graph and join them
6x + 2y – 16 => 6x = 16 – 2y
x = 162y6
x = 8y3 (Dividing by 2)
Substituting some different values of y, we get their corresponding values of x as shown below:
Solution Of RD Sharma Class 10 Chapter 3 Pair Of Linear Equations In Two Variables
Now plot the points and point them
We see that the two lines coincide with each other
This system has infinitely many solutions
RD Sharma Class 10 Book Pdf Chapter 3 Pair Of Linear Equations In Two Variables

Question 14.
x- 2y + 11 = 0
3x – 6y + 33 = 0
Solution:
x – 2y + 11 = 0
x = 2y – 11
Substituting some different values of y, we get their corresponding values of x as shown below
RD Sharma 10 Chapter 3 Pair Of Linear Equations In Two Variables
Plot the points on the graph and join them 3x – 6y + 33 = 0
3x = 6y – 33
x = 6y333
Substituting some different values of y, we get corresponding values of x as shown below
RD Sharma 10 Chapter 3 Pair Of Linear Equations In Two Variables
Plot the points on the graph and join them we see that the two lines coincide with each other
This system has infinitely many solutions.
10th Maths Solution Book Pdf Chapter 3 Pair Of Linear Equations In Two Variables
Show graphically that each one of the following systems of equations is inconsistent (i.e., has no solution)

Question 15.
3x – 5y = 20
6x – 10y = -40 (C.B.S.E. 1995C)
Solution:
3x – 5y = 20
3x = 20 + 5y
x = 20+5y3
Substituting some different values of y, we get their corresponding values of x as shown below
Maths RD Sharma Class 10 Solutions Chapter 3 Pair Of Linear Equations In Two Variables
Plot the points on the graph and join them
6x – 10y = -40
6x = 10y – 40
x = 10y406
Substituting some different values of y, we get their corresponding values of x as shown below
Maths RD Sharma Class 10 Solutions Chapter 3 Pair Of Linear Equations In Two Variables
Plot the points on the graph and join them we see that the lines are parallel
The given system of equations is inconsistent and has no solution.
RD Sharma Class 10 Textbook PDF Chapter 3 Pair Of Linear Equations In Two Variables

Question 16.
x – 2y = 6
3x – 6y = 0 (C.B.S.E. 1995)
Solution:
x – 2y = 6
x = 6 + 2y
Substituting some different values of y, we get their corresponding values of x as shown below:
RD Sharma Class 10 Textbook PDF Chapter 3 Pair Of Linear Equations In Two Variables
Plot the points on the graph and join them
3x – 6y = 0
=> 3x = 6y
=> x = 2y
Substituting some different values of y, we get their corresponding values of x as shown below:
RD Sharma Class 10 Textbook PDF Chapter 3 Pair Of Linear Equations In Two Variables
Plot the points on the graph and join them We see that the lines are parallel
The system of equations is inconsistent and therefore has no solution.
RD Sharma 10 Class Solutions Chapter 3 Pair Of Linear Equations In Two Variables

Question 17.
2y – x = 9
6y – 3x = 21 (C.B.S.E. 1995C)
Solution:
2y – x = 9
=> x = 2y – 9
Substituting some different values of y, we get their corresponding values of x as shown below:
RD Sharma Maths Class 10 Solutions Chapter 3 Pair Of Linear Equations In Two Variables
Now plot the points on the graph and join them
6y – 3x = 21
=> 6y = 21 + 3x
y = 21+3x6
Substituting some different values of x, we get their corresponding values of y as shown below:
RD Sharma Maths Class 10 Solutions Chapter 3 Pair Of Linear Equations In Two Variables
Now plot the points on the graph and join them we see that the lines are parallel
The system of equations is inconsistent and therefore has no solution.
RD Sharma Maths Class 10 Solutions Chapter 3 Pair Of Linear Equations In Two Variables

Question 18.
3x – 4y – 1 = 0
2x – 83 y + 5 = 0
Solution:
3x – 4y -1 = 0
3x = 4y + 1
x = 4y+13
Substituting some different values of y, we get their corresponding values of x as shown below:
Class 10 RD Sharma Chapter 3 Pair Of Linear Equations In Two Variables
Now plot the points on the graph and join them
2x – 83 y + 5 = 0
=> 6x – 8y + 15 = 0
=> 6x = 8y – 15
=> x = 8y156
Now substituting some different values of y, we get their corresponding values of x as shown below
Class 10 RD Sharma Chapter 3 Pair Of Linear Equations In Two Variables
Plot the points on the graph and join them We see that the lines are parallel
The system of equations is inconsistent Therefore has no solution.
Class 10 RD Sharma Chapter 3 Pair Of Linear Equations In Two Variables

Question 19.
Determine graphically the vertices of the triangle the equations of whose sides are given below :
(i) 2y – x = 8, 5y – x = 14 and y – 2x = 1 (C.B.S.E. 1994)
(ii) y = x, y = 0 and 3x + 3y = 10 (C.B.S.E. 1994)
Solution:
(i) Equations of the sides of a triangle are 2y – x = 8, 5y – x = 14 and y – 2x = 1
2y – x = 8
x = 2y – 8
Substituting some different values of y, we get their corresponding values of x as shown below
RD Sharma Class 10 Book Pdf Free Download Chapter 3 Pair Of Linear Equations In Two Variables
Now plot the points and join them Similarly in 5y – x = 14
x = 5y – 14
RD Sharma Class 10 Book Pdf Free Download Chapter 3 Pair Of Linear Equations In Two Variables
Now plot these points and join them in each case
We see that these lines intersect at (-4, 2), (1, 3), and (2, 5) which are the vertices of the triangle so formed.
RD Sharma Class 10 Book Pdf Free Download Chapter 3 Pair Of Linear Equations In Two Variables
(ii) y = x, y = 0 and 3x + 3y = 10
y = x
Substituting some different values of x, we get their corresponding values of y, as shown below
RD Sharma Class 10 Book Pdf Free Download Chapter 3 Pair Of Linear Equations In Two Variables
RD Sharma Class 10 Book Pdf Free Download Chapter 3 Pair Of Linear Equations In Two Variables

Question 20.
Determine graphically whether the system of equations x – 2y = 2, 4x – 2y = 5 is consistent or in-consistent ?
Solution:
x – 2y = 2
x = 2y + 2
Substituting some values of y, we get their corresponding values of x, as shown below
RD Sharma Maths Class 10 Solutions Pdf Free Download Chapter 3 Pair Of Linear Equations In Two Variables
Now plot the points on the graph and join them
4x – 2y = 5
4x = 2y + 5
x = 2y+54
Substituting some different values of y, we get their corresponding values bf x as shown below
RD Sharma Maths Class 10 Solutions Pdf Free Download Chapter 3 Pair Of Linear Equations In Two Variables
Now plot the above points and join them We see that there two lines intersect each other
The system is consistent
RD Sharma Maths Class 10 Solutions Pdf Free Download Chapter 3 Pair Of Linear Equations In Two Variables

Question 21.
Determine by drawing graphs, whether the following system of linear equations has a unique solution or not :
(i) 2x – 3y = 6, x + y = 1 (C.B.S.E. 1994)
(ii) 2y = 4x – 6, 2x = y + 3 (C.B.S.E. 1995C)
Solution:
(i) 2x – 3y = 6, x + y = 1
2x – 3y = 6
=> 2x = 6 + 3y
=> x = 6+3y2
Substituting some different values of y, we get their corresponding values of x show below
RD Sharma Maths Class 10 Solutions Pdf Free Download Chapter 3 Pair Of Linear Equations In Two Variables
Now plot the points and join them
x + y = 1 => x = 1 – y
Substituting some different of y, we get their corresponding value of x as given below
RD Sharma Class 10 Pdf Ebook Chapter 3 Pair Of Linear Equations In Two Variables
Now plot the points on the graph and join them we see that the lines intersect at a point
This system has a unique solution.
RD Sharma Class 10 Pdf Ebook Chapter 3 Pair Of Linear Equations In Two Variables
(ii) 2y = 4x – 6, 2x = y + 3
2y = 4x – 6
y = 4x62 = 2x – 3
Substituting some different values of x, we get their corresponding values of y as shown below
RD Sharma Class 10 Pdf Ebook Chapter 3 Pair Of Linear Equations In Two Variables
Now plot the points on the graph and join them
2x = y + 3
x = y+32
Substituting some different values of y, we get their corresponding values of x as shown below
RD Sharma Class 10 Pdf Ebook Chapter 3 Pair Of Linear Equations In Two Variables
Plot the points on the graph and join them We see the lines coincide each other
This system has no unique solution.
RD Sharma Class 10 Pdf Ebook Chapter 3 Pair Of Linear Equations In Two Variables

Question 22.
Solve graphically each of the following systems of linear equations. Also And the coordinates of the points where the lines
meet axis of y.
(i) 2x – 5y + 4 = 0
2x + y – 8 = 0 (C.B.S.E. 2005)
(ii) 3x + 2y = 12
5x – 2y = 4 (C.B.S.E. 2000C)
(iii) 2x + y – 11 = 0
x – y – 1=0 (C.B.S.E. 2000C)
(iv) x + 2y – 7 = 0
2x – y – 4 = 0 (C.B.S.E. 2000C)
(v) 3x + y – 5 = 0
2x – y – 5 = 0 (C.B.S.E. 2002C)
(vi) 2x – y – 5 = 0
x – y – 3 = 0 (C.B.S.E. 2002C)
Solution:
(i) 2x – 5y + 4 = 0, 2x – 5y + 4 = 0
2x – 5y + 4 = 0 ⇒ 2x = 5y – 4
⇒ x = 5y42
Substituting some different values of y, we get their corresponding values of x as shown here
RD Sharma Class 10 Solution Chapter 3 Pair Of Linear Equations In Two Variables
Now plot the points on the graph and join them
2x + y – 8 = 0 => 2x = 8 – y
x = 8y2
Substituting some different values of y, we get their corresponding values of x as shown below
RD Sharma Class 10 Pdf Free Download Full Book Chapter 3 Pair Of Linear Equations In Two Variables
Now join these points and join them
We see that the lines intersect each other at (3, 2)
x = 3, y = 2
These line intersect y-axis at(0, 45) and (0, 8) respectively.
RD Sharma Class 10 Pdf Free Download Full Book Chapter 3 Pair Of Linear Equations In Two Variables
(ii) 3x + 2y = 12, 5x – 2y = 4
3x + 2y = 12
=> 3x = 12 – 2y
x = 122y3
Substituting some different values of y, we get their corresponding values of x as shown below
RD Sharma Class 10 Pdf Free Download Full Book Chapter 3 Pair Of Linear Equations In Two Variables
Now plot the points and join them Similarly in 5x – 2y = 4
=> 5x = 4 + 2y
x = 4+2y5
RD Sharma Class 10 Pdf Free Download Full Book Chapter 3 Pair Of Linear Equations In Two Variables
Now join these points and join them
We sec that these lines intersect each other at (2, 3)
x = 2, y= 3
These lines intersect the y-axis at (0, 6) and (0, 2) respectively.
Class 10 RD Sharma Solutions Chapter 3 Pair Of Linear Equations In Two Variables
(iii) 2x + y – 11 = 0, x – y – 1 = 0
2x + y – 11 = 0 => y = 11 – 2x
Substituting some different values of x, we get their corresponding values of y as shown below:
Class 10 RD Sharma Solutions Chapter 3 Pair Of Linear Equations In Two Variables
Now plot the points and join them Similarly in x – y – 1= 0 => x = y + 1
Class 10 RD Sharma Solutions Chapter 3 Pair Of Linear Equations In Two Variables
Now plot the points and join them We see that these two lines intersect each other at (4, 3) and intersect the y-axis at (0, 11) and (0,-1)
Class 10 RD Sharma Solutions Chapter 3 Pair Of Linear Equations In Two Variables
(iv) x + 2y – 7 = 0, 2x – y – 4 = 0
x + 2y – 7 = 0
x = 7 – 2y
Substituting some different values of y, we get their corresponding values of x as shown below
Learncbse.In Class 10 Chapter 3 Pair Of Linear Equations In Two Variables
Now plot these points and join them Similarly in
2x – y – 4 = 0
y = 2x – 4
Learncbse.In Class 10 Chapter 3 Pair Of Linear Equations In Two Variables
Now plot these points and join them We see that these two lines intersect each other at (3, 2)
and these lines intersect the y-axis at (0, 72) and (0, -4)
RD Sharma Solutions Class 10 Chapter 3 Pair Of Linear Equations In Two Variables
(v) 3x + y – 5 = 0, 2x – y – 5 = 0
3x + y – 5= 0
y = 5 – 3x
Substituting some different values of x, we get corresponding values of y as shown below
RD Sharma Class 10 Pdf Chapter 3 Pair Of Linear Equations In Two Variables
Now plot these points and join them Similarly in 2x – y – 5 = 6 => y = 2x – 5
RD Sharma Class 10 Pdf Chapter 3 Pair Of Linear Equations In Two Variables
Now plot these points and join them We see that these two lines intersect each other at (2, -1)
x = 2, y = 1
and these Lines intersect the y-axis at (0, 5) and (0, -5) respectively.
RD Sharma Class 10 Pdf Chapter 3 Pair Of Linear Equations In Two Variables
(vi) 2x – y – 5 = 0, x – y – 3 = 0
2x – y – 5 = 0
y = 2x – 5
Substituting some different values of x, we get their corresponding values of y as shown below
RD Sharma Class 10 Solutions Chapter 3 Pair Of Linear Equations In Two Variables
Plot the points and join them Similarly in-the equation x – y – 3 = 0 => x =y + 3
RD Sharma Class 10 Solutions Chapter 3 Pair Of Linear Equations In Two Variables
Plot these points on the graph and join them we see that these two lines intersect each other at (2, -1)
x = 2, y = 1
and these lines intersect y-axis at (0, -5) and (0, -3)
RD Sharma Class 10 Solutions Chapter 3 Pair Of Linear Equations In Two Variables

Question 23.
Solve the following system of linear equations graphically and shade the region between the two lines and x-axis
(i) 2x + 3y = 12, x – y = 1 (C.B.S.E. 2001)
(ii) 3x + 2y – 4 = 0, 2x – 3y – 7 = 0 (C.B.S.E. 2006C)
(iii) 3x + 2y – 11 = 0, 2x – 3y + 10 = 0 (C.B.S.E. 2006C)
Solution:
(i) 2x + 3y = 12, x – y = 1
2x + 3y = 12 => 2x = 12 – 3y
=> x = 123y2
Substituting some different values of y, we get corresponding values of x as shown below
rd-sharma-class-10-solutions-chapter-3-pair-of-linear-equations-in-two-variables-ex-3-2-23
Now plot the points on the graph and join them. Similarly in the equation
x – y = 1 => x = 1 + y
RD Sharma Class 10 Solutions Chapter 3 Pair Of Linear Equations In Two Variables
Now plot the points on the graph and join them
We see the two lines intersect each other at (3, 2) and intersect also x-axis at (6, 0) and 0,0)
The required region has been shaded.
RD Sharma Class 10 Solutions Chapter 3 Pair Of Linear Equations In Two Variables
(ii) 3x + 2y – 4 = 0, 2x – 3y – 7 = 0
3x + 2y – 4 = 0
=> 3x = 4 – 2y
x = 42y3
Substituting some different values of y, we get corresponding values of x as shown below
RD Sharma Class 10 Solutions Pair Of Linear Equations In Two Variables
Now plot the points on the graph and join them. Similarly in the equation
2x – 3y – 7 = 0
=> 2x = 3y + 7
=> x = 3y+72
RD Sharma Class 10 Solutions Pair Of Linear Equations In Two Variables
Plot these points and join them
The required region is surrounded by these two lines and the x-axis has been shaded as shown.
RD Sharma Class 10 Solutions Pair Of Linear Equations In Two Variables
(iii) 3x + 2y – 11 = 0, 2x – 3y + 10 = 0
3x + 2y – 11
=> 3x = 11 – 2y
=> x = 112y3
Substituting some different values of y, we get corresponding values of x as shown below
RD Sharma Class 10 Solutions Pair Of Linear Equations In Two Variables
Now plot the points and join them. Similarly in the equation
2x – 3y + 10 = 0
2x = 3y – 10
x = 3y102
RD Sharma Class 10 Solutions Pair Of Linear Equations In Two Variables
Now plot the points and join them
The required region surrounded by these two lines and Y-axis has been shaded as shown.
RD Sharma Class 10 Solutions Pair Of Linear Equations In Two Variables

Question 24.
Draw the graphs of the following equations on the same graph paper :
2x + 3y =12
x – y = 1
Find the coordinates of the vertices of the triangle formed by the two straight lines and the y-axis. (C.B.S.E. 2001)
Solution:
2x + 3y = 12
⇒ 2x = 12 – 3y
x = 123y2
Substituting some different values of y, we get corresponding values of x as shown below
Pair Of Linear Equations In Two Variables Class 10 RD Sharma
Now plot the points on the graph and join them. Similarly in the equation
x – y = 1 => x = y + 1
Pair Of Linear Equations In Two Variables Class 10 RD Sharma
Now plot the points on the graph and join them
The required region surrounded by these two lines and y-axis has been shaded as shown
Pair Of Linear Equations In Two Variables Class 10 RD Sharma

Question 25.
Draw the graphs of x – y + 1 = 0 and 3x + 2y – 12 = 0. Determine the coordinates of the vertices of the triangle formed by these lines and x-axis and shade the triangular area. Calculate the area bounded by these lines and x-axis. (C.B.S.E. 2002)
Solution:
x – y + 1 =0, 3x + 2y-12 = 0
x – y + 1 = 0
x = y – 1
Substituting some different values of y, we get so their corresponding values of x as shown below :
Pair Of Linear Equations In Two Variables Class 10 RD Sharma
Now plot the points and join them Similarly, in the equation
3x + 2y – 12 = 0 => 3x = 12 – 2y
x = 122y3
RD Sharma Class 10 Chapter 3 Pair Of Linear Equations In Two Variables
Plot the points on the graph and join them. These two lines intersect each other at (2, 3) and x-axis at (-1, 0) and (4, 0)
Area of the triangle ABC = 12 x Base x Altitude
RD Sharma Class 10 Chapter 3 Pair Of Linear Equations In Two Variables

Question 26.
Solve graphically the system of linear equations :
4x – 3y + 4 = 0
4x + 3y – 20 = 0
Find the area bounded by these lines and the x-axis. (C.B.S.E. 2002)
Solution:
4x – 3y + 4 = 0
=> 4x = 3y – 4
=> x = 3y44
Substituting some different values of y, we get their corresponding values of x as shown below:
RD Sharma Class 10 Chapter 3 Pair Of Linear Equations In Two Variables
RD Sharma Class 10 Chapter 3 Pair Of Linear Equations In Two Variables

Question 27.
Solve the following system of linear equations graphically 3x + y – 11 = 0, x – y – 1 = 0. Shade the region bounded by these lines and the y-axis. Also, find the area of the region bounded by these lines and the y-axis. (C.B.S.E. 2002C)
Solution:
3x + y – 11=0
y = 11 – 3x
Substituting some different values of x, we get their corresponding values of y as shown below :
RD Sharma Class 10 Solutions Pair Of Linear Equations In Two Variables
Now plot these points on the graph and join them Similarly in the equation
x – y – 1 = 0
=> x = y + 1
RD Sharma Class 10 Solutions Pair Of Linear Equations In Two Variables
Now plot these points on the graph and join them. We see that these two lines intersect each other at point (3,2)
x = 3, y = 2
Now shade the region enclosed by these two lines and the y-axis
RD Sharma Class 10 Pdf Chapter 3 Pair Of Linear Equations In Two Variables
Area of shaded ∆ABC
12 x AC x BD
12 x 12 x 3 = 18 sq. units

Question 28.
Solve graphically each of the following systems of linear equations. Also, find the coordinates of the points where the lines meet the axis of x in each system.
(i) 2x + y = 6
x – 2y = -2 (C.B.S.E. 1998)
(ii) 2x – y = 2
4x – y = 8 (C.B.S.E. 1998)
(iii) x + 2y = 5
2x – 3y = -4 (C.B.S.E. 2005)
(iv) 2x + 3y = 8
x – 2y = -3 (C.B.S.E. 2005)
Solution:
(i) 2x + y = 6, x – 2y = -2
2x + y = 6
y = 6 – 2x
Substituting some different values of x, we get their corresponding values of y as shown below
Learncbse.In Class 10 Chapter 3 Pair Of Linear Equations In Two Variables
Now plot the points and join them Similarly in the equation
x – 2y = -2
=> x = 2y – 2
Learncbse.In Class 10 Chapter 3 Pair Of Linear Equations In Two Variables
Now plot the points and join them We see that these two lines intersect each other at (2, 2)
x = 2, y = 2
Here two lines also meet the x-axis at (3, 0) and (-2, 0) respectively as shown in the figure.
Learncbse.In Class 10 Chapter 3 Pair Of Linear Equations In Two Variables
(ii) 2x – y = 2, 4x – y = 8
2x – y = 2
=> y = 2x – 2
Substituting some different values of x, we get corresponding values of y as shown below:
RD Sharma Class 10 Pdf Free Download Full Book Chapter 3 Pair Of Linear Equations In Two Variables
Now plot the points on the graph and join them Similarly in the equation
4x – y = 8
=> y = 4x – 8
RD Sharma Class 10 Pdf Free Download Full Book Chapter 3 Pair Of Linear Equations In Two Variables
Now plot these points and join them We see that these two lines intersect each other at (3, 4)
x = 3, y = 4
These two lines also meet the x-axis at (1, 0) and (2,0) respectively as shown in the figure
RD Sharma Class 10 Pdf Free Download Full Book Chapter 3 Pair Of Linear Equations In Two Variables
(iii) x + 2y = 5, 2x – 3y = -4
x + 2y = 5
=> x = 5 – 2y
Substituting some different values of y, we get their corresponding values of x as shown below
RD Sharma Class 10 Pdf Ebook Chapter 3 Pair Of Linear Equations In Two Variables
Now plot the points on the graph and join them
Similarly in the equation
2x – 3y = 4
=> 2x = 3y – 4
x = 3y42
RD Sharma Class 10 Pdf Ebook Chapter 3 Pair Of Linear Equations In Two Variables
Plot these points and join them
We see that these two lines intersect each other at (1, 2)
x = 1, y = 2
and these two lines meet the x-axis at (5, 0) and (-2, 0) respectively as shown in the figure
RD Sharma Class 10 Pdf Ebook Chapter 3 Pair Of Linear Equations In Two Variables
(iv) 2x + 3y = 8, x – 2y = -3
2x + 3y = 8
=> 2x = 8 – 3y
x = 83y2
Substituting some different values of y, we get their corresponding values of x as shown below:
RD Sharma Class 10 Book Pdf Free Download Chapter 3 Pair Of Linear Equations In Two Variables
Plot these points on the graph and join them Similarly in the equation
x – 2y = -3
x = 2y – 3
RD Sharma Class 10 Book Pdf Free Download Chapter 3 Pair Of Linear Equations In Two Variables
Now plot these points and join them We see that these two lines intersect each other at (1, 2)
x = 1, y = 2
and also these lines meet the x-axis at (4, 0) and (-3, 0) respectively as shown in the figure
RD Sharma Class 10 Book Pdf Free Download Chapter 3 Pair Of Linear Equations In Two Variables

Question 29.
Draw the graphs of the following equations 2x – 3y + 6 = 0
2x + 3y – 18 = 0
y – 2 = 0
Find the vertices of the triangle so obtained. Also, find the area of the triangle.
Solution:
2x – 3y + 6 = 0
2x = 3y – 6
x = 3y62
Substituting some different values of y, we get their corresponding values of x as shown below:
RD Sharma Maths Class 10 Solutions Chapter 3 Pair Of Linear Equations In Two Variables
Now plot these points on the graph and join them
Similarly in the equation 2x + 3y -18 = 0
=> 2x = 18 – 3y
x = 183y2
RD Sharma Maths Class 10 Solutions Chapter 3 Pair Of Linear Equations In Two Variables
and in equation y – 2 = 0
y = 2
Which is parallel to the x-axis on its positive side Now plot the points and join them We see that these lines intersect each other at (3, 4), (6, 2), and (0, 2)
Area of the triangle ABC, so formed
12 x base x altitude
12 x BC x AD
12 x 6 x 2
= 6 sq. units
RD Sharma Maths Class 10 Solutions Chapter 3 Pair Of Linear Equations In Two Variables

Question 30.
Solve the following system of equations graphically:
2x – 3y + 6 = 0
2x + 3y – 18 = 0
Also, find the area of the region bounded by these two lines and the y-axis.
Solution:
2x – 3y + 6 = 0
2x = 3y – 6
x = 3y62
Substituting some different values of y, we get their corresponding values of x as shown below:
RD Sharma Class 10 Textbook PDF Chapter 3 Pair Of Linear Equations In Two Variables
Plot these points on the graph and join them Similarly in the equation
2x + 3y – 18 = 0
=> 2x = 18 – 3y
x = 183y2
RD Sharma Class 10 Textbook PDF Chapter 3 Pair Of Linear Equations In Two Variables
Plot these points on the graph and join them. We see that these two lines intersect each other at (3, 4)
x = 3, y = 4
These lines formed a triangle ABC with the y-axis
Area of ∆ABC = 12 x base x altitude
12 x BC x AD
12 x 4 x 3 = 6 Sq. units
RD Sharma Class 10 Textbook PDF Chapter 3 Pair Of Linear Equations In Two Variables

Question 31.
Solve the following system of linear equations graphically :
4x – 5y – 20 = 0
3x + 5y – 15 = 0
Determine the vertices of the triangle formed by the lines representing the above equation and the y-axis. (C.B.S.E. 2004)
Solution:
4x – 5y – 20 = 0
=> 4x = 5y + 20
x = 5y+202
Substituting some different values of y, we get their corresponding values of x as shown below
10th Maths Solution Book Pdf Chapter 3 Pair Of Linear Equations In Two Variables
Plot these points on the graph and join them Similarly in the equation
3x + 5y – 15 = 0
=> 3x = 15 – 5y
x = 155y2
10th Maths Solution Book Pdf Chapter 3 Pair Of Linear Equations In Two Variables
Now plot these points and join them We see that these two lines intersect each other at (5, 0)
x = 5, y = 0
These two lines form an ∆ABC with a y-axis whose vertices are A (5, 0), B (0, 3), C (0, -4)
10th Maths Solution Book Pdf Chapter 3 Pair Of Linear Equations In Two Variables

Question 32.
Draw the graphs of the equations 5x – y = 5 and 3x – y = 3. Determine the coordinates of the vertices of the triangle formed by these lines and the y-axis calculate the area of the triangle so formed.
Solution:
5x – y = 5
=> y = 5x – 5
Substituting some different values of x, we get their corresponding values of y as shown below:
RD Sharma Class 10 Book Pdf Chapter 3 Pair Of Linear Equations In Two Variables
Plot these points on the graph and join them. Similarly in the equation
3x – y = 3
=> y = 3x – 3
RD Sharma Class 10 Book Pdf Chapter 3 Pair Of Linear Equations In Two Variables
Now plot these points and join them We see that these two lines intersect each other at (1, 0)
RD Sharma Class 10 Book Pdf Chapter 3 Pair Of Linear Equations In Two Variables
RD Sharma 10 Solutions Chapter 3 Pair Of Linear Equations In Two Variables

Question 33.
Form the pair of linear equations in the following problems, and find their solution graphically.
(i) 10 students of class X took part in the Mathematics quiz. If the number of girls is 4 more than the number of boys, find the number of boys and girls who took part in the quiz.
(ii) 5 pencils and 7 pens together cost Rs. 50, whereas 7 pencils and 5 pens together cost Rs. 46. Find the cost of one pencil and a pen.
(iii) Champa went to a ‘sale’ to purchase some pants and skirts. When her friends asked her how many of each she had bought, she answered, “The number of skirts is two less than twice the number of pants purchased. Also, the number of skirts is four less than four times the number of pants purchased.” Help her friends to find how many pants and skirts Champa bought. [NCERT]
Solution:
Let number of boys = x
and number of girls = y
According to the given conditions
x + y = 10
y – x = 4
Now, x + y = 10
=> x = 10 – y
Substituting some different values of y, we get their corresponding values of x as given below
RD Sharma 10 Solutions Chapter 3 Pair Of Linear Equations In Two Variables
Plot the points on the graph and join them Similarly in the equation
y – x = 4
=> y = 4 + x
RD Sharma Class 10 Maths Chapter 3 Pair Of Linear Equations In Two Variables
Now plot the points and join them we see that these two lines intersect each other at (3, 7)
x = 3, y = 7
Number of boys = 3
and number of girls = 7
RD Sharma Class 10 Maths Chapter 3 Pair Of Linear Equations In Two Variables
(ii) Let cost of 1 pencil = Rs. x
and cost of 1 pen = Rs. y
According to the given conditions,
5x + 7y = 50
2x + 5y = 46
5x + 7y = 50
5x = 50 – 7y
x = 507y5
Substituting some different values of y, we get the corresponding values of x as given below
RD Sharma Class 10 Maths Chapter 3 Pair Of Linear Equations In Two Variables
Plot these points and join them Similarly in the equation
7x + 5y = 46
=> 7x = 46 – 5y
=> x = 465y7
Class 10 RD Sharma Pdf Chapter 3 Pair Of Linear Equations In Two Variables
Now plot the points on the graph and join them. We see that these two lines intersect each other at (3, 5)
x = 3, y = 5
or cost of pencil = Rs. 3
and cost of a pen = Rs. 5
Class 10 RD Sharma Pdf Chapter 3 Pair Of Linear Equations In Two Variables
(iii) Let number of skirts = x
and number of pants = y
According to the given condition,
x = 2y – 2 and x = 4y – 4
2y – 2 = 4y – 4
4y – 2y = -2 + 4
2y = 2
y = 1
and x = 2y – 2 = 2 x 1 – 2 = 2 – 2 = 0
Number of skirts = 0
and number of pants = 1

Question 34.
Solve the following system of equations graphically shade the region between the lines and the y -axis
(i) 3x – 4y = 7
5x + 2y = 3 (C.B.S.E. 2006C)
(ii) 4x – y = 4
3x + 2y = 14 (C.B.S.E. 2006C)
Solution:
(i) 3x – 4y = 7
3x = 7 + 4y
x = 7+4y3
Substituting some different values of y, we get their corresponding values of x as shown below
Class 10 RD Sharma Pdf Chapter 3 Pair Of Linear Equations In Two Variables
Plot these points on the graph and join them. Similarly in the equation
5x + 2y = 3
=> 5x = 3 – 2y
x = 32y5
Answers Of RD Sharma Class 10 Chapter 3 Pair Of Linear Equations In Two Variables
Plot these points and join them We see that the lines intersect each other at (1, -1)
x = 1, y = -1
Now the region between these lines and the y-axis has been shaded as shown
Answers Of RD Sharma Class 10 Chapter 3 Pair Of Linear Equations In Two Variables
(ii) 4x – y = 4
3x + 2y = 14
4x – y = 4
y = 4x – 4
Substituting some different values of x, we get their corresponding values of y as given below
Answers Of RD Sharma Class 10 Chapter 3 Pair Of Linear Equations In Two Variables
Plot these points and join them Similarly in equation
3x + 2y = 14
3x = 14 – 2y
x = 142y3
RD Sharma Maths Book For Class 10 Solution Chapter 3 Pair Of Linear Equations In Two Variables
Now plot these points and join them
We see that these lines intersect each other at (2, 4)
x = 2, y = 4
The region between these two lines and the y-axis has been shaded as shown
RD Sharma Maths Book For Class 10 Solution Chapter 3 Pair Of Linear Equations In Two Variables

Question 35.
Represent the following pair of equations graphically and write the coordinates of points where the lines intersects y-axis
x + 3y = 6
2x – 3y = 12 (C.B.S.E. 2008)
Solution:
x + 3y = 6
x = 6 – 3y
Substituting some different values of y, we get their corresponding values of x as shown below
RD Sharma Maths Book For Class 10 Solution Chapter 3 Pair Of Linear Equations In Two Variables
Now plot these points on the graph and join them
Similarly in the equation
2x – 3y = 12 => 2x = 12 + 3y
x = 12+3y2
RD Sharma Maths Book For Class 10 Solution Chapter 3 Pair Of Linear Equations In Two Variables
Now plot their points and join them We see that these two lines meet the y-axis at (0, 2) and (0, -4)
10th Maths Solution Book Pdf Chapter 3 Pair Of Linear Equations In Two Variables

Question 36.
Given the linear equation 2x + 3y – 8 = 0, write another linear equation in two variables such that the geometrical representation of the pair so formed is
(i) intersecting lines
(ii) Parallel lines
(iii) coincident lines [NCERT]
Solution:
Given a linear equation 2x + 3y – 8 = 0
(i) When the lines are intersecting, then
10th Maths Solution Book Pdf Chapter 3 Pair Of Linear Equations In Two Variables

Question 37.
Determine graphically the co-ordinates of the vertices of a triangle, the equations of whose sides are :
(i) y = x, y = 2x and y + x = 6 (C.B.S.E. 2000)
(ii) y = x, 3y = x, x + y = 8 (C.B.S.E. 2000)
Solution:
(i) y = x
Substituting some different values of x, we get their corresponding values of y as shown below
10th Maths Solution Book Pdf Chapter 3 Pair Of Linear Equations In Two Variables
Now plot the points on the graph and join them. Similarly in the equation y = 2x
RD Sharma Class 10 Pdf Free Download Full Book Chapter 3 Pair Of Linear Equations In Two Variables
and y + x = 6 => x = 6 – y
RD Sharma Class 10 Pdf Free Download Full Book Chapter 3 Pair Of Linear Equations In Two Variables
Now plot the points on the graph and join them. We see that these lines intersect each other at (0, 0), (3, 3), and (2, 4)
Vertices of the triangle so formed by these lines are (0, 0), (3, 3), and (2, 4)
RD Sharma Class 10 Pdf Free Download Full Book Chapter 3 Pair Of Linear Equations In Two Variables
(ii) y = x, 3y = x, x + y = 8
y = x
Substituting some different values of x, we get corresponding values of y as shown below
Class 10 RD Sharma Chapter 3 Pair Of Linear Equations In Two Variables
Plot these points on the graph and join them Similarly in the equation 3y = x
Class 10 RD Sharma Chapter 3 Pair Of Linear Equations In Two Variables
and x + y = 8 => x = 8 – y
Class 10 RD Sharma Chapter 3 Pair Of Linear Equations In Two Variables
Now plot the points and join them. We see that these lines intersect each other at (0,0), (4, 4), (6, 2)
The vertices of the triangle so formed are (0, 0), (4, 4), and (6, 2)
RD Sharma Maths Class 10 Solutions Pdf Free Download Chapter 3 Pair Of Linear Equations In Two Variables

Question 38.
Graphically, solve the following pair of equations:
2x + y = 6
2x – y + 2 = 0
Find the ratio of the areas of the two triangles formed by the lines representing these equations with the x-axis and the lines with the y-axis. [NCERT Exemplar]
Solution:
Given equations are 2x + y – 6 and 2x – y + 2 = 0
Table for equation 2x + y = 6
RD Sharma Maths Class 10 Solutions Pdf Free Download Chapter 3 Pair Of Linear Equations In Two Variables
RD Sharma Maths Class 10 Solutions Pdf Free Download Chapter 3 Pair Of Linear Equations In Two Variables
Learncbse.In Class 10 Chapter 3 Pair Of Linear Equations In Two Variables
Hence, the pair of equations intersect graphically at point E (1, 4), i.e., x = 1 and y = 4

Question 39.
Determine, graphically, the vertices of the triangles formed by the lines y = x, 3y = x, x + y = 8. [NCERT Exemplar]
Solution:
Given linear equations are y = x …….(i)
3y = x ………(ii)
and x + y = 8 …….(iii)
For equation y = x,
If x = 1, then y = 1
If x = 0, then y = 0
If x = 2, then y = 2
Table for line y = x,
Learncbse.In Class 10 Chapter 3 Pair Of Linear Equations In Two Variables
For equation x = 3y
If x = 0, then y = 0,
if x = 3, then y = 1
and if x = 6, then y = 2
Table for line x = 3y,
RD Sharma Class 10 Solutions Chapter 3 Pair Of Linear Equations In Two Variables
For equation,
If x = 0, then y = 8
if x = 8, then y = 0
and if x = 4, then y = 4
Table for line x + y = 8,
RD Sharma Class 10 Solutions Chapter 3 Pair Of Linear Equations In Two Variables
Plotting points A (1, 1) and B (2,2), we get the straight line AB. Plotting the points C (3, 1) and D (6, 2), we get the straight line CD. Plotting the points P (0, 8), Q (4, 4), and R (8, 0), we get the straight line PQR. We see that lines AB and CD intersecting the line PR on Q and D, respectively.
So, ∆OQD is formed by these lines. Hence, the vertices of the ∆OQD formed by the given lines are O (0, 0), Q (4, 4), and D (6, 2).
RD Sharma Class 10 Solutions Chapter 3 Pair Of Linear Equations In Two Variables

Question 40.
Draw the graph of the equations x = 3, x = 5 and 2x – y – 4 = 0. Also, find the area of the quadrilateral formed by the lines and the x-axis. |NCERT Exemplar]
Solution:
Given equation of lines 2x – y – 4 = 0, x = 3 and x = 5
Table for line 2x – y – 4 = 0,
RD Sharma Class 10 Solutions Chapter 3 Pair Of Linear Equations In Two Variables
Draw the points P (0, -4) and Q (2,0) and join these points and form a line PQ also draw the lines x = 3 and x = 5.
Area of quadrilateral ABCD = 12 x distance between parallel lines (AB) x (AD + BC) [since, quadrilateral ABCD is a trapezium]
12 x 2 x (6 + 2) [∵ AB = OB – OA = 5 – 3 = 2, AD = 2 and BC = 6]
= 8 sq. units
RD Sharma Class 10 Solution Chapter 3 Pair Of Linear Equations In Two Variables
Hence, the required area of the quadrilateral formed by the lines and the x-axis is 8 sq. units.

Question 41.
Draw the graphs of the lines x = -2, and y = 3. Write the vertices of the figure formed by these lines, the x-axis and the y-axis. Also, find the area of the figure. [NCERT Exemplar]
Solution:
We know that the graph of x = -2 is a line parallel to the y-axis at a distance of 2 units to the left of it. So, the line l is the graph of x = -2
RD Sharma Class 10 Solution Chapter 3 Pair Of Linear Equations In Two Variables
The graph of y = 3 is a line parallel to the x-axis at a distance of 3 units above it.
So, the line m is the graph of y = 3
The figure enclosed by the line x = -2, y = 3, the x-axis, and the y-axis is OABC, which is a rectangle.
A is a point on the y-axis at a distance of 3 units above the x-axis. So, the coordinates of A are (0, 3).
C is a point on the x-axis at a distance of 2 units to the left of the y-axis. So, the coordinates of C are (-2, 0).
B is the solution of the pair of equations x = -2 and y = 3. So, the coordinates of B are (-2, 3).
So, the vertices of the rectangle OABC are O (0, 0), A (0, 3), B (-2, 3), C (-2, 0).
The length and breadth of this rectangle are 2 units and 3 units, respectively.
As the area of a rectangle = length x breadth, the area of rectangle OABC = 2 x 3 = 6 sq. units.

Question 42.
Draw the graphs of the pair of linear equations x – y + 2 = 0 and 4x – y – 4 = 0. Calculate the area of the triangle formed by the lines so drawn and the x-axis. [NCERT Exemplar]
Solution:
For drawing the graphs of the given equations, we find two solutions of each of the equations, which are given in the table.
Plot the points A (0,2), B (-2,0), P (0, -4), and Q (1,0) on the graph paper, and join the points to form the lines AB and PQ as shown in the figure.
RD Sharma Class 10 Solution Chapter 3 Pair Of Linear Equations In Two Variables
We observe that there is a point R (2,4) common to both the lines AB and PQ. The triangle formed by these lines and the x-axis is BQR.
The vertices of this triangle are B (-2, 0), Q (1, 0), and R (2, 4).
We know that;
Area of triangle = 12 x Base x Altitude
Here, Base = BQ = BO + OQ = 2 + 1 = 3 units
Altitude = RM = Ordinate of R = 4 units.
So, area of ABQR = 12 x 3 x 4 = 6 sq. units

We have provided complete details of RD Sharma Class 10 Solutions Chapter 3 Exercise 3.2. If you have any queries related to CBSE Class 10, feel free to ask us in the comment section below.

FAQs on RD Sharma Class 10 Solutions Chapter 3 Exercise 3.2

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Yes, all of the questions in RD Sharma Class 10 Solutions Chapter 3 Exercise 3.2 must be learned. These questions may appear on both board exams and class tests. Students will be prepared for their board exams if they learn these questions.

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1. Correct answers according to the last CBSE guidelines and syllabus.
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