Form the pair of linear equations in the following problem, and find their solutions (if they exist) by the elimination method :

Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. How old are Nuri and Sonu?

Let present age of Nuri be x years and age of Sonu be y years.

Given,

Five years ago, Nuri was thrice as old as Sonu.

⇒ (x - 5) = 3(y - 5)

⇒ x - 5 = 3y - 15

⇒ x - 3y - 5 + 15 = 0

⇒ x - 3y + 10 = 0 ……..(1)

Given,

Ten years later, Nuri will be twice as old as Sonu.

⇒ (x + 10) = 2(y + 10)

⇒ x + 10 = 2y + 20

⇒ x - 2y + 10 - 20 = 0

⇒ x - 2y - 10 = 0 ……..(2)

Subtracting equation (1) from equation (2), we get :

⇒ x - 2y - 10 - (x - 3y + 10) = 0

⇒ x - 2y - 10 - x + 3y - 10 = 0

⇒ y - 20 = 0

⇒ y = 20.

Substituting value of y in equation (1), we get :

⇒ x - 3(20) + 10 = 0

⇒ x - 60 + 10 = 0

⇒ x - 50 = 0

⇒ x = 50.

Hence, pair of linear equations are x - 3y + 10 = 0, x - 2y - 10 = 0, where x and y are the ages (in years) of Nuri and Sonu respectively; Age of Nuri (x) = 50, Age of Sonu (y) = 20.