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

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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