Skip to content
Related Articles

Related Articles

Improve Article
Save Article
Like Article

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

  • Last Updated : 21 Feb, 2021

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

Attention reader! All those who say programming isn't for kids, just haven't met the right mentors yet. Join the  Demo Class for First Step to Coding Coursespecifically designed for students of class 8 to 12. 

The students will get to learn more about the world of programming in these free classes which will definitely help them in making a wise career choice in the future.

And, the present age of his daughter = y



Seven years ago,

Age of Aftab = x-7

Age of his daughter = y-7

Three years after,

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:

xy
06
-420

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:

xy
0-2
60

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



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:

xy
0650
13000

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:

xy
100400
13000

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



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:

xy
0160
800

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:

xy
0150
750

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

My Personal Notes arrow_drop_up
Recommended Articles
Page :

Start Your Coding Journey Now!