## Chapter 3 Pair of Linear Equations in Two Variables Ex 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:**

Let present age of Aftab = x years and present age of Aftab’s daughter = y years.

**1st Condition :** Seven years ago

x – 7 = 7(y – 7)

⇒ x – 7 = 7y – 49

⇒ x – 7y = – 42

**Table :**

2nd Condition :

Three years later,

2nd Condition :

x + 3 = 3(y + 3)

x + 3 = 3y + 9

x – 3y = 6

**Table :**

Thus, the algebraic equations are

x – 7y + 42 = 0 and x – 3y – 6 = 0

**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:**

Let cost of one bat = ₹ x

and the cost of one ball = ₹y **A.T.Q.** **1st Condition :** 3x + 6y = 3900

**Table :**

2nd Condition :

2nd Condition :

x + 3y = 1300

**Table :**

Thus, the algebraic equations are 3x + 6y = 3900 and x + 3y – 1300

**Question 3.**

The cost of 2 kg of apples and 1 kg 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:**

Let cost of one kg of apples = ₹ x and the cost of one kg of grapes = ₹y

**A.T.Q.** **1st Condition :**

2x + y = 160 **Table :2nd Condition :**

4x + 2y = 300

**Table :**

Thus, algebraic situations are 2x + y = 160 and 4x + 2y = 300