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**Q.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: **Let the present age of Aftab be ‘x’.

And, the present age of his daughter be ‘y’.

Now, we can write, seven years ago,

Age of Aftab = x - 7

Age of his daughter = y - 7

According to the question, x − 7 = 7(y − 7)

⇒ x − 7 = 7y − 49

⇒ x − 7y = −42 ………………………(i)

Also, three years from now or after three years,

Age of Aftab will become = x + 3.

Age of his daughter will become = y + 3

According to the situation given,

x + 3 = 3(y + 3)

⇒ x + 3 = 3y + 9

⇒ x − 3y = 6 …………..…………………(ii)

Subtracting equation (i) from equation (ii) we have

(x − 3y) − (x − 7y) = 6 − (−42)

⇒ −3y + 7y = 6 + 42

⇒ 4y = 48

⇒ y = 12

The algebraic equation is represented by

x − 7y = −42

x − 3y = 6

For, x − 7y = −42 or x = −42 + 7y

For, x − 3y = 6 or x = 6 + 3y

**Q.2. The coach of a cricket team buys 3 bats and 6 balls for Rs.3900. Later, she buys another bat and 3 more balls of the same kind for Rs.1300. Represent this situation algebraically and geometrically.Solution: **Let us assume that the cost of a bat be ‘Rs x’

And, the cost of a ball be ‘Rs y’

According to the question, the algebraic representation is

3x + 6y = 3900

And x + 3y = 1300

For, 3x + 6y = 3900

Or x = (3900 - 6y) / 3

For, x + 3y = 1300

Or x = 1300 - 3y

Solution:

And, cost of 1 kg of grapes be ‘Rs. y’

According to the question, the algebraic representation is

2x + y = 160 And 4x + 2y = 300

For, 2x + y = 160 or y = 160 − 2x, the solution table is;

For 4x + 2y = 300 or y = (300 - 4x) / 2, the solution table is;

**Check out the NCERT Solutions of all the exercises of Linear Equations in Two Variables: **

Ex 3.2 NCERT Solutions: Pair of Linear Equations in Two Variables

Ex 3.3 NCERT Solutions: Pair of Linear Equations in Two Variables

Ex 3.4 NCERT Solutions: Pair of Linear Equations in Two Variables

Ex 3.5 NCERT Solutions: Pair of Linear Equations in Two Variables

Ex 3.6 NCERT Solutions: Pair of Linear Equations in Two Variables

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132 docs

- Ex 3.2 NCERT Solutions: Pair of Linear Equations in Two Variables
- Ex 3.3 NCERT Solutions: Pair of Linear Equations in Two Variables
- Ex 3.4 NCERT Solutions: Pair of Linear Equations in Two Variables
- Additional Question-Answers: Pair of Linear Equations in Two Variable
- Value-Based Questions: Pair of Linear Equations in Two Variables
- Facts That Matter: Pair of Linear Equations in Two Variables