( x, y) satisfies both equations y+18=x(x-3) and x=y+6

(- 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 )

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