ShmoopTube

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Here's another shmoop du jour.

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The following graph represents the solution set to which of the following systems of inequalities in two variables?

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Here are the potential answers…

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Ok sooo… what in the world is a solution set, first of all?

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Well, it’s the set of all points that answers a given equation.

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Like… if the inequalty was “x is greater than 0,” then the whole right side of a

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graph would be shaded in like this…

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From the graph, we can see that one line is dotted, while the other is solid.

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We know that a “less than” or “greater than” inequality without the “equals to”

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signifies a dotted line…

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…and that a “less than or equal to” and a “greater than or equal to” inequality

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signifies a solid line.

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So, because we have one of each in our graph, we know our answer solution has to have one

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inequality with an equals sign and one without.

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We can immediately eliminate A and D.

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The dotted line has the equation y equals -x + 3, and in the graph, the shaded region

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is above this line.

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So we know the inequality must be “y is GREATER THAN negative x plus 3.”

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Only B has this inequality, and we're good.

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That's it. Answer B.

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