Question

Shade the solution set to the system of inequalities.*Picture include*

x+2y>-5
2x+y<=2

Is the answer, A, B,C, or D?

http://i46.tinypic.com/2m76yp2.jpg

Answer 1

First, plot the corresponding equation of each inequality by using = instead of > or <=.
Plot x + 2y = -5. Use a dashed line for this one because the inequality sign is simply > and not >=.
The dashed line x + 2y = -5 separates the plane into two regions. Test one point in either region to see if it makes the original inequality true. If it does, that's the region you shade.
Then do the same with the other inequality. Plot the corresponding equation, but this time with a solid line becasue you have <=. Then test a point in one region to see if it works in the original second inequality. If it does, that's the region you shade. If not, shade the other region.
The region that is shaded by both inequalities is the solution.

Answer 2

Start with the first inequality:
x + 2y > -5
Corresponding equation is:
x + 2y = -5
Plot by points.
Let x = 0, 0 + 2y = -5; 2y = -5; y = -2.5
Let y = 0, x + 2(0) = -5; x = -5
The two points are (0. -2.5) and (-5, 0)