Graph the system of inequalities. a) Graph b) Shade the solutions of the system of inequalities. c) Explain what the solution (shaded area) represents.

Question

Graph the system of inequalities.

a) Graph

x+2y<7

y>=-x-1

b) Shade the solutions of the system of inequalities.

c) Explain what the solution (shaded area) represents.

Answer 1

This will be hard to show in a chat box, but here goes.

 

To graph an inequality, you must first graph the corresponding EQUATION. For this problem, they are x+2y = 7 and y = -x-1. The graphs of these are straight lines. You should already know how to graph them. The first one should be drawn with a DASHED (DOTTED) line, since the line is NOT part of the actual graph. The second one should be drawn with a SOLID line, as the line itself is part of the graph.

 

The next step will be, for each equation, to choose a point NOT on the line, and plug it into the original inequality to see if it makes it true or false. IF TRUE, shade the side of the line containing the point; IF FALSE, shade the opposite side of the line.

 

After you do this for both equations, you will have a graph with two lines and one side of each shaded. The answer is the common region shaded in both. It will look like a quadrant, but probably with sides not parallel to the axes.

 

As for the third question, I will let you think about it. You can post a reply later if you still need help.