NCERT Solutions for class 10 maths chapter 3

Pair of Linear Equations in Two Variables

NCERT Solutions for class 10 maths chapter 3 Exercise 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.

Answer

Let the present age of Aftab be x
And his daughter be y.
Seven years ago,
Age of Aftab = x-7
Age of his daughter = y-7
According to question
x−7 = 7(y−7)
x−7 = 7y−49
x−7y = −42 ......(1)
After three years
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)
The algebraic equation is represented by
x−7y = −42
x−3y = 6
For, x−7y = −42
or x = −42+7y

Question 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.

Answer

Let the cost of a bat be Rs x
the cost of a ball be Rs y
According to the question
3x+6y = 3900
x+3y = 1300
3x+6y = 3900

Question 3

The cost of 2 kg of apples and 1kg 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 be Rs. y
According to the question,
2x+y = 160
4x+2y = 300
For, 2x+y = 160
y = 160−2x