(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 )
