Answer:
(- 5, 10 ) and (- 1, 6 )
Step-by-step explanation:
Given the 2 equations
y = x² + 5x + 10 → (1)
y = - x + 5 → (2)
Substitute y = x² + 5x + 10 into (2)
x² + 5x 6+ 10 = - x + 5 ( subtract - x + 5 from both sides )
x² + 6x + 5 = 0 ← in standard form
(x + 1)(x + 5) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 1 = 0 ⇒ x = - 1
x + 5 = 0 ⇒ x = - 5
Substitute these values into (2) for corresponding values of y
x = - 5 : y = - (- 5) + 5 = 5 + 5 = 10 ⇒ (- 5, 10 )
x = - 1 : y = - (- 1) + 5 = 1 + 5 = 6 ⇒ (- 1, 6 )
