Answer:
(- 4, - 2 ) and (2, 4 )
Step-by-step explanation:
Given the 2 equations
y = x² + 3x - 6 → (1)
y = x + 2 → (2)
Substitute y = x² + 3x - 6 into (2)
x² + 3x - 6 = x + 2 ( subtract x + 2 from both sides )
x² + 2x - 8 = 0 ← in standard form
(x + 4)(x - 2) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 4 = 0 ⇒ x = - 4
x - 2 = 0 ⇒ x = 2
Substitute these values into (2) for corresponding values of y
x = - 4 → y = - 4 + 2 = - 2 ⇒ (- 4, - 2 )
x = 2 → y = 2 + 2 = 4 ⇒ (2, 4 )
