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
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 42 years and age of his son is 10 years.