Question

What is one of the solutions to the following system of equations? y2 + x2 = 53 and y − x = 5

Answer 1

y2 + x2 = 53
y − x = 5
y = 5 + x

(5+x)^2 + x^2 = 53
(5+x)(5+x) + x^2 = 53
25 + 10x + x^2 +x^2 = 53
2x^2 + 10x - 28 = 0
(x-2)(x+7)=0
x = 2 , x = - 7

y = 5 + 2
y = 7

y = 5 +(-7)
y = 5 - 7
y = - 2