Linear equations in two variables – Exercise 3.1 – Class 10

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 = 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 then, Age of Aftab = x + 3

Age of his daughter = y + 3

According to the question

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

x = 3 = 3y + 9

x – 3y = 6 ———-(2)

Thus, the algebraic expression is

x – 7y = -42

x –  3y = 6

For, x – 7y = -42

x = -42 + 7y

x -7 0 7
y 5 6 7

 

For x – 3y = 6

x =  6+3y

The solution table is

x 6 3 0
y 0 -1   -2

The graphical representation of the

1.png


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 the cost of a bat be Rs x and the cost of a ball = Rs y

According to the question, the algebraic representation is 

3x + 6y = 3900

x + 2y = 1300

For 3x + 6y = 3900

x = (3900-6y)/3                      

x 300 100 -100
y 500 600 700

For, x + 2y = 1300

x = 1300 -2y

The solution table is

x 300 100 -100
y 500 600 700

The graphical representation is,

2.png


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.

Solution:

 Let the cost of 1 kg of apples be Rs x and the cost of 1 kg of grapes = Rs y

According to the question, the algebraic representation is 

2x + y  = 160

4x + 3y = 300

For 2x + y = 160

y = 160 – 2x

The solution table is

 

For 4x + 2y = 300

x 50 60 70
y 60 40 20

 

y = (300-4x)/2

The solution table is

x 70 80 75
y 10 -10 0

3.png

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