Class 10 Maths


Linear Equations

NCERT 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. Represent this situation algebraically and graphically.

Answer: Let us assume Aftab’s current age = x and his daughter’s current age = y

Seven years ago:

Aftab’s age = x - 7 and daughter’s age = y - 7

As per question, seven years ago, Aftab was seven times as old as his daughter was seven years ago.

So, x – 7 = 7(y – 7)

Solving this equation, we get

x – 7 = 7y – 49

Or, x = 7y – 49 + 7

Or, x = 7y – 42

Or, 7y – x – 42 = 0 ……(1)

This equation gives following values for x and y

x = - 35, - 28, - 21, - 14, - 7, 0, 7, 14, 21, 28, 35, 42, 49

y = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13

Three years from now:

Aftab’s age = x + 3 and daughter’s age = y + 3

As per question, three years from now, Aftab will be thtice as old as his daughter.

So, x + 3 = 3(y + 3)

Or, x + 3 = 3y + 9

Or, x = 3y + 9 – 3

Or, x = 3y + 6

Or, 3y – x + 6 = 0 ……..(2)

This equation gives following values for x and y:

x = 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45

y = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13

The following graph is plotted for the given pair of linear equations:

linear equations exercise Answer

The lines for x and y intersect at point representing the coordinates (12, 42)

So, daughter’s age = 12 years and Aftab’s age = 42 years

Question 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.

Answer: Let us assume that price of one bat = x and price of one ball = y. Following equations can be written as per the question:

Price of 3 bats and 6 balls:

3x + 6y = 3900

Or, x + 2y = 1300 ……..(1)

This equation will give following values for x and y

x 1500, 1400, 1300, 1200, 1100
y - 100, - 50, 0, 50, 100

Now, price of 1 bat and 3 balls:

x + 3y = 1300 ……….(2)

This equation will give following values for x and y

x 1600, 1450, 1300, 1150, 1000
y - 100, - 50, 0, 50, 100

The following graph is plotted for the given pair of linear equations.

linear equations exercise Answer

The lines for x and y intersect at point representing the coordinates (1300, 0)

So, Price of one bat = Rs. 1300 and Price of one ball = zero

Question 3: The cost of 2 kg apples and 1 kg grapes was found to be Rs. 160. After a month, the cost of 4 kg apples and 2 kg grapes is Rs. 300. Represent this situation algebraically and graphically.

Answer: Let us assume that cost of 1 kg apple = x and cost of 1 kg grapes = y. Following equations can be written as per the question.

2x + y = 160 ……..(1)

This equation gives following values for x and y

x 70, 60, 50, 40
y 20, 40, 60, 80

4x + 2y = 300

Or, 2x + y = 150 ……..(2)

This equation will give following values for x and y:

x 65, 55, 45, 35
y 20, 40, 60, 80

The following graph is plotted for the given pair of linear equations.

linear equations exercise Answer

Since we get parallel lines so there will be no Answer for this pair of linear equations.