##### NCERT-Class X-Mathematics

01-Real Numbers

02-Polynomials

03-Pair of Linear Equations in Two Variables

04-Quadratic Equations

05-Arithmetic Progression

06-Triangles

07-Coordinate Geometry

08-Introduction to Trigonometry

09-Some Applications of Trigonometry

10-Circles

11-Constructions

12-Area Related to Circles

13-Surface Areas and Volumes

14-Statistics

15-Probability

### Chapter 03-Pair of Linear Equations in Two Variables-Exercise Solutions

NCERT Book Page No 44: Exercise 3.1

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.

Answer: Let the present age of Aftab be x.

And, present age of his daughter = y

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 ————————-(1)

Three years hence,

Age of Aftab = x + 3

Age of his daughter = y + 3

According to the question,

(x+3)=3(y+3)

x+3 = 3(y +3)

x-3y =6 —————-(2)

Therefore, the algebraic representation is

x-7y= -42

x-3y=6

For x-7y = -42,

X = -42 + 7y

The solution table is

For x -3y =6 ,

X = 6 +3y

The solution table is

The graphical representation is as follows.

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

Solution: Let cost of one bat = Rs x

Cost of one ball = Rs y

3 bats and 6 balls for Rs 3900 So that

3 x + 6y = 3900 ———————(1)

Divide complete equation by 3 we get

x + 2y = 1300

Subtract 2y both side we get

x = 1300 – 2y

Plug y = – 1300, 0 and 1300 we get

x = 1300 – 2 ( – 1300 ) = 1300 + 2600 = 3900

x= 1300 -2(0) = 1300 -0 = 1300

x= 1300 – 2(1300) = 1300 – 2600 = – 1300

Given that she buys another bat and 2 more balls of the same kind for Rs 1300

So we get

x + 2 y = 1300 ———————(2)

Subtract 2y both side we get

x = 1300 – 2y

Plug y = – 1300, 0 and 1300 we get

x = 1300 – 2 ( – 1300 ) = 1300 + 2600 = 3900

X = 1300 – 2 ( 0 ) = 1300 – 0 = 1300

X = 1300 – 2(1300) = 1300 – 2600 = -1300

Algebraic representation

3 x + 6 y = 3900 ———————(1)

x + 2 y = 1300 ———————(2)

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

Answer: Let the cost of 1 kg of apples be Rs x.

And, cost of 1 kg of grapes = Rs y

According to the question, the algebraic representation is

2x + y =160

4x +2y = 300

For 2x +y =160,

y= 160- 2x

The solution table is

For 4x + 2y = 300,

$ y= \frac{300-4x}{2}$

The solution table is

The graphical representation is as follows.