Given : x + y = 99 ------------ [1]
Given : x² - y² = 99
We know that : (x² - y²) = (x + y)(x - y)
⇒ (x + y)(x - y) = 99
⇒ 99(x - y) = 99
⇒ x - y = 1 ------------- [2]
Adding Equation [1] and [2], we get :
⇒ (x + y) + (x - y) = 99 + 1
⇒ 2x = 100
⇒ x = 50
Substituting x = 50 in Equation [1], we get :
⇒ 50 + y = 99
⇒ y = 99 - 50
⇒ y = 49
So, The Ordered pair (x , y) = (50 , 49)