I'm trying to solve x^2+7x+y+8 =0 and -10x^2-59x+y-91=0 my teacher gives us the answer which is (-3,4) but she wants us to set it up as y=? and do it that way

Thank you for the opportunity to help you with your question!

First step: isolate the y in both equations

y(1)=-x^2-7x-8

y(2)=10x^2+59x+91

With y on only one side of the equation, what we're really being asked to do is find the values of x for which y(1) is equal to y(2). And then we solve for what that value is :)

Set them equal:

y(1)=y(2), or

-x^2 -7x -8 = 10x^2 +59x +91

Isolate x on one side:

-7x - 8 = 11x^2 + 59x + 91

-8 = 11x^2 + 66x + 91

11x^2 + 66x + 99 = 0

11(x^2 + 6x + 9) = 0

x^2 + 6x + 9 = 0

(x+3)(x+3)= 0

x = -3

Solve either equation for x = -3:

y(1) = - (-3)^2 - 7(3) - 8 = -12 - 8 = 4 :)

(-3, 4)

Please let me know if you need any clarification. I'm always happy to answer your questions.