Solve each solution by substitution. y=-x^2-2x+8 y=x^2-8x-12

(5, - 27) and ( - 2, 8)

Since both equations express y in terms of x , we can equate the right sides

x² - 8x - 12 = - x² - 2x + 8

rearrange into standard form ( ax² + bx + c = 0 )

2x² - 6x - 20 = 0 ( divide through by 2 )

x² - 3x - 10 = 0

(x - 5)(x + 2) = 0 ( equate each factor to zero and solve for x )

x - 5 = 0 ⇒ x = 5

x + 2 = 0 ⇒ x = -2

Substitute these values into either of the 2 equations for y

x = - 5 → y = 25 - 40 - 12 = - 27 ( using x² - 8x - 12 )

x = - 2 → y = 4 + 16 - 12 = 8

solutions : (5, - 27) or ( - 2, 8 )