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

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

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.

Yess thank you!

To graph the solution set of the system of inequalities, we first need to graph each inequality separately and then find the intersection points.

1. Graph the inequality:
y > x^2 - 8

a. Start by graphing the equation y = x^2 - 8. This is a parabola that opens upward.

b. To determine if the inequality is greater than (>) or greater than or equal to (≥), we test a point on either side of the parabola.

For example, let's test the point (0, 0). Substitute the coordinates into the inequality: 0 > (0)^2 - 8. Simplifying, we get 0 > -8, which is true. This means the region above the parabola is shaded.

2. Graph the inequality:
x + y ≤ 1

a. First, graph the equation x + y = 1. This is a straight line with a slope of -1 and a y-intercept of 1.

b. Since the inequality is "less than or equal to" (≤), we need to shade the region below the line.

3. Find the intersection points of the related equations:

a. Find the points where the two equations intersect by solving the system.

Substitute y = x^2 - 8 into the inequality x + y ≤ 1:
x + (x^2 - 8) ≤ 1

b. Rearrange the equation and solve for x:
x^2 + x - 9 ≤ 1
x^2 + x - 10 ≤ 0
(x - 2)(x + 5) ≤ 0

c. The solutions for x are x = -5 and x = 2.

d. Substitute these x-values back into the first equation y = x^2 - 8 to find the corresponding y-values:
For x = -5: y = (-5)^2 - 8 = 17
For x = 2: y = (2)^2 - 8 = -4

e. The intersection points are (-5, 17) and (2, -4).

So, based on the calculations, the intersection points of the related equations are (-5, 17) and (2, -4), which are different from the points you provided.