Graph the solution set of the system of inequalities and give the exact coordinates of the intersection points of the related equations:

Question

y>x^2 -8
X+y≤1,

The closest points I'm getting is (-2.5,-1.8) and (2.5,-1.5) but I feel like they're incorrect

Answer 1

let's test your answers by graphing the equations.
http://www.wolframalpha.com/input/?i=plot+y%3Dx%5E2+-8,++x%2By%3D1

hover your cursor over the intersection points, and it shows that you are incorrect.

x+y=1 ---> y = 1- x

y = x^2 - 8
x^2 - 8 = 1 - x
x^2 + x - 9 = 0
x = (-1 ± √37)/2
= appr 2.54 or x = -3.54

sub into y = 1-x to find the intersection points

I assume you know how to graph the region.

Answer 2

Yess thank you!