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Question 136250: This problem is coming from a worksheet and states to solve the problem by graphing. Can you please help with solving and graphing the problem? Note: There is a line under the greater/less than signs.
Thank you.
{y > x + 2
{2x + 3y < -9
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website! Replace the inequality signs with equal signs. Then graph both of the lines. Put the inequality signs back. Since both of your inequality signs include "or equal" the lines you have drawn should be solid (if they were just < or >, you would used dashed lines)
Now you have to figure out which side of each line to shade. For each line, pick a point NOT on the line. Doesn't matter where, and generally, if the line doesn't pass through the origin (and neither of these do) I pick (0,0) because that makes the arithmetic easy. Now substitute the values of the x- and y-coordinates for x and y in your inequality. If you have a true statement, shade in the entire half-plane on the side of the line containing your point. If you have a false statement, color in the other side.
The solution set will be that area of the graph where the shaded parts intersect, that is, that part of the graph that is covered by shading from both inequalities.
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