Question

Solve the system of equations.
y=-4x
y = x2 – 12

Answer 1

(- 6, 24 ) and (2, - 8 )

Explanation:

Given the 2 equations

y = - 4x → (1)

y = x² - 12 → (2)

Substitute y = x² - 12 into (1)

x² - 12 = - 4x ( add 4x to both sides )

x² + 4x - 12 = 0 ← in standard form

(x + 6)(x - 2) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 6 = 0 ⇒ x = - 6

x - 2 = 0 ⇒ x = 2

Substitute these values into (1) for corresponding values of y

x = - 6 : y = - 4(- 6) = 24 ⇒ (- 6, 24 )

x = 2 : y = - 4(2) = - 8 ⇒ (2, - 8 )