Answer:
(- 3, 12 ) and (5, 28 )
Step-by-step explanation:
Given the 2 equations
y = x² + 3 → (1)
y - 2x = 18 → (2)
Substitute y = x² + 3 into (2)
x² + 3 - 2x = 18 ( subtract 18 from both sides )
x² - 2x - 15 = 0 ← in standard form
(x + 3)(x - 5) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 3 = 0 ⇒ x = - 3
x - 5 = 0 ⇒ x = 5
Substitute these values into (1) for corresponding values of y
x = - 3 : y = (- 3)² + 3 = 9 + 3 = 12 ⇒ (- 3, 12 )
x = 5 : y = 5² + 3 = 25 + 3 = 28 ⇒ (5, 28 )
