Form the pair of linear equations in the following problems and find their solutions graphically. Two years ago, a father was five times as old as his son. Two years later, his age will be 8 more than three times the age of the son.

Let the present age of father = x year

and the present age of his son = y year

Two years ago,

Father’s age = (x – 2) year

His son’s age = (y – 2) year

According to the question,

⇒ (x – 2) = 5(y – 2)

⇒ x – 2 = 5y – 10

⇒ x – 5y + 8 = 0 …(1)

After two years,

Father’s age = (x + 2) year

His son’s age = (y + 2) year

According to the question,

⇒ (x + 2) = 3(y + 2) + 8

⇒ x + 2 = 3y + 6 + 8

⇒ x – 3y – 12 = 0 …(2)

Now, table for x – 5y + 8 = 0

Now, table for x – 3y – 12 = 0

On plotting points on a graph paper and join them to get a straight line representing x – 5y + 8 = 0.

Similarly, on plotting the points on the same graph paper and join them to get a straight line representing x – 3y – 12 = 0.

∴ x = 42, y = 10 is the solution of the pair of linear equations.

Hence, the age of father is 42years and age of his son is 10 years.