Question

What are the solutions to the following system y = −x2 +2x − 9 y = −6x + 6

Answer 1

y = -x^2 + 2x - 9
y = -6x + 6

-6x + 6 = -x^2 + 2x - 9
x^2 - 2x + 9 - 6x + 6 = 0
x^2 - 8x + 15 = 0
(x - 5)(x - 3) = 0

x - 5 = 0 y = -6x + 6
x = 5 y = -6(5) + 6
y = -30 + 6
y = -24

x - 3 = 0 y = -6x + 6
x = 3 y = -6(3) + 6
y = -18 + 6
y = -12

solutions are : (5,-24) , (3,-12)