Math I need help

Question

The sun of two numbers is -5, and the sun of squares of two numbers is 17. What are the two numbers? Explain your reasoning.

Answer 1

x + y = -5

x^2 + y^2 = 17

x = -5-y

(-5-y)^2 + y^2 = 17

y^2 + 10y + 25 +y^2 = 17

2y^2 + 10y + 8 = 0

y^2 + 5y + 4 = 0

(y+4)(y+1) = 0

y = -1, -4

x = -4, -1

the two numbers are -1 and -4