Question

What is the ordered pair or real numbers for which x + y = 99 and x^2 - y^2 = 99.

Answer 1

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)