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    Inequalities

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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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    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 ...

    $2.49

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