Solve each linear-quadratic system algebraically. Show all work.

y = - x^2 + 2x + 7

y = - 2x + 2

(5, - 8) and ( - 1, 4)

Step-by-step explanation:

Given the 2 equations

y = - x² + 2x + 7 → (1)

y = - 2x + 2 → (2)

Substitute y = - 2x + 2 into (1)

- 2x + 2 = - x² + 2x + 7 ← subtract - x² + 2x + 7 from both sides

x² - 4x - 5 = 0 ← in standard form

(x - 5) (x + 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 5 = 0 ⇒ x = 5

x + 1 = 0 ⇒ x = - 1

Substitute these values into (2) for corresponding values of y

x = 5 → y = - 2 (5) + 2 = - 10 + 2 = - 8 ⇒ (5, - 8)

x = - 1 → y = - 2 ( - 1) + 2 = 2 + 2 = 4 ⇒ ( - 1, 4)