What is one of the solutions to the following system of equations?. y2 + x2 = 65. y + x = 7

X^2+y^2=65

(x+y) = 7 = > y=7-x

substitute in first equation

x^2 + ((7-x) ^2=65

expand and simplify

x^2+x^2-14x+49=65

2x^2-14x-16=0

2 (x^2-7x-8) = 0

Factorize

2 (x-8) (x+1) = 0

x=8, or x=-1

take x=8, solve for y=+/-1

Take y=+/-1, x=+/-8

So the solutions are

{8,1},{-8,-1},{8,-1},{-8,1

Out of these, only {8,-1} satisfies x+y=7, so this is the only solution.