Question

Please please help!! I rlly need to pass this test

Find the solution(s) of the system of equations.

y = -x^2 + 2
y = x^2 + 4x + 4

Answer 1

x = -1

y = 1

Explanation:

y = -x² + 2 (1)

y = x² + 4x + 4 (2)

matching (2) and (1);

-x² + 2 = x² + 4x + 4

-x² - x² - 4x + 2 - 4 = 0

-2x² - 4x - 2 = 0

-x² - 2x - 1 = 0

x² + 2x + 1 = 0

(x + 1)² = 0

x + 1 = 0

x = -1

replacing in (1)

y = - x² + 2

y = - (-1)² + 2

y = -1 + 2

y = 1

Verification;

-x² + 2 = x² + 4x + 4

-(-1)² + 2 = (-1)² + 4(-1) +4

-1 + 2 = 1 - 4 + 4

1 = 1 ✔