Answer:
(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)
