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18. match the system of inequalities to a region in the picture

x + 2y <= 8
3x - 2y <= 0

22. solve the system of linear inequalities graphically

3x + 4y <= 12
y >= -3

32. solve the system of linear inequalities graphically, find the coordinates of each corner points, and indicate whether the solution region is bounded or unbounded

3x + 4y <= 24
x >= 0
y >= 0

38. solve the system of linear inequalities graphically, find the coordinates of each corner points, and indicate whether the solution region is bounded or unbounded

3x + y <=21
x + y <= 9
x >= 0
y >= 0

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#### Solution Preview

18. match the system of inequalities to a region in the picture

x + 2y <= 8
3x - 2y <= 0

In this question, and in all the other ones, I'm first going to put the inequalities in slope-intercept format. In the second inequality, notice that you have to switch the direction of the sign when dividing both sides by -2.

x + 2y <= 8 3x - 2y <= 0
2y <= -x + 8 -2y <= -3x
y <= (-1/2)x + 4 y >= (3/2)x

For the first inequality, you'd shade below the line with a slope of -1/2 and a y-intercept of 4. For the second inequality, you'd shade below the line with a slope of 3/2 and a y-intercept of 0.

The region that satisfies both these conditions is region ...

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