Question

What are the x-coordinates to the solutions of the system of equations:

x + y + 10 = 0
x ^ 2 + y - 2 = 0

A) x = - 4, -3

B) x= 4, 14

C) x= -3, 4

D) x= -3, -7

Answer 1

C

Explanation:

x + y + 10 = 0 ( subtract x + 10 from both sides )

y = - x - 10 → (1)

x² + y - 2 = 0 → (2)

substitute y = - x - 10 into (2)

x² - x - 10 - 2 = 0

x² - x - 12 = 0 ← in standard form

(x - 4)(x + 3) = 0 ← in factored form

equate each factor to zero and solve for x

x + 3 = 0 ⇒ x = - 3

x - 4 = 0 ⇒ x = 4