Answer:
(- 2, - 8 ) , (6, 0 )
Step-by-step explanation:
y + 18 = x(x - 3) ← distribute
y + 18 = x² - 3x → (1)
x = y + 6 → (2)
Substitute x = y + 6 into (1)
y + 18 =(y + 6)² - 3(y + 6) ← expand parenthesis using FOIL
y + 18 = y² + 12y + 36 - 3y - 18
y + 18 = y² + 9y + 18 ( subtract y + 18 from both sides )
0 = y² + 8y = y(y + 8)
Equate each factor to zero and solve for y
y = 0
y + 8 = 0 ⇒ y = - 8
Substitute these values into (2) and evaluate for x
y = 0 : x = 0 + 6 = 6 ⇒ (6, 0 )
y = - 8 : x = - 8 + 6 = - 2 ⇒ (- 2, - 8 )
