Class 10 NCERT Solutions- Chapter 3 Pair of Linear Equations in Two Variables - Exercise 3.1

Question 1. Aftab tells his daughter, “Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be.” (Isn’t this interesting?) Represent this situation algebraically and graphically.

Solution:

Present age of Aftab = x

And, the present age of his daughter = y

,

Age of Aftab = x-7

Age of his daughter = y-7

Age of Aftab = x+3

Age of his daughter = y+7

Here, According to the given condition,

x−7 = 7(y−7)

x−7 = 7y−49

x−7y = −42         ………………………(I)

To draw the line for Eqn. (I), we need at least two solutions of the equation, So, we can use the following table to draw the graph:

x	y
0	6
-42	0

And, According to the another given condition,

x+3 = 3(y+3)

x+3 = 3y+9

x−3y = 6       …………..…………………(II)

To draw the line for Eqn. (II), we need at least two solutions of the equation, So, we can use the following table to draw the graph:

x	y
0	-2
6	0

The graphical representation of Eqn. (I) and Eqn. (II) is:

👁 Image

Question 2. The coach of a cricket team buys 3 bats and 6 balls for ₹ 3900. Later, she buys another bat and 3 more balls of the same kind for ₹1300. Represent this situation algebraically and geometrically.

Solution:

The cost of a bat = ₹ x

And, the cost of a ball = ₹ y

Here, According to the Given condition,

3x+6y = 3900 .........................(I)

x+3y = 1300 .........................(II)

To draw the line for Eqn. (I), we need at least two solutions of the equation, So, we can use the following table to draw the graph:

x	y
0	650
1300	0

To draw the line for Eqn. (II), we need at least two solutions of the equation, So, we can use the following table to draw the graph:

x	y
100	400
1300	0

The graphical representation of Eqn. (I) and Eqn. (II) is:

👁 Image

Question 3. The cost of 2 kg of apples and 1kg of grapes on a day was found to be ₹ 160. After a month, the cost of 4 kg of apples and 2 kg of grapes is ₹300. Represent the situation algebraically and geometrically. 

Solution:

The cost of 1 kg of apples = ₹ x

And, cost of 1 kg of grapes = ₹ y

Here, According to the given conditions,

2x+y = 160 ...........................(I)

4x+2y = 300 ...........................(II)

To draw the line for Eqn. (I), we need at least two solutions of the equation, So, we can use the following table to draw the graph:

x	y
0	160
80	0

To draw the line for Eqn. (II), we need at least two solutions of the equation, So, we can use the following table to draw the graph:

x	y
0	150
75	0

The graphical representation of Eqn. (I) and Eqn. (II) is:

👁 Image

Summary

Exercise 3.1 of Chapter 3 (Pair of Linear Equations in Two Variables) in NCERT Class 10 Mathematics introduces the concept of linear equations in two variables and their graphical representation. It covers topics such as identifying linear equations, determining whether a given pair of equations forms a consistent or inconsistent system, and graphing linear equations. Students learn to plot linear equations on a coordinate plane, interpret the nature of their solutions based on the graphs, and understand the geometric significance of different types of solutions (one solution, no solution, or infinitely many solutions).