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Question 724251: Shade the solution set to the system of inequalities
x + 3y > -2
2x + y less than or equal to 2
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! 
We need to graph the line for  as a dashed line to show that the points on that line are not part of the solution.
We need to graph part of the line for  as a solid line to show that those points are part of the solution.
We need two points to determine each line, and I will find points that are easy to calculate and give me a good graph.
For ,
 -->  gives us point (-2,0)
 -->  -->  -->  gives us point (4,-2)
For ,
 -->  gives us point (0,2)
-->  -->  gives us point (1,0)
Those two points are a bit too close together, but may still give us a decent graph.
Seeing the lines plotted may make what follows easier.
 The solution will include all the points inside one of the four angles formed by the lines.
Using a test point that is not part of the lines would allow us to see if that point is on the same side of each line as the solution.
The easiest test point is (0,0), the origin, with and
Substituting, we find that (0,0) is part of the solution for both inequalities:
 and 
So we shade the wedge that contains the origin, and plot the lines, dashed and solid as needed.
 The intersection of the two lines is not part of the solution.
Its coordinates satisfy the equations of both lines, including , but it do not satisfy the inequality  .
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