Systems of Inequalities

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What is a system of inequalities?

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A system of inequalities is a set of two or more inequalities with the same variables. The solution is the region where the graphs of the inequalities overlap.

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How do you determine if a point is a solution to a system of inequalities?

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To determine if a point is a solution, substitute the point's coordinates into each inequality. If the point satisfies all inequalities, it is a solution.

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What does a dotted line represent in a graph of an inequality?

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A dotted line indicates that the points on the line are not included in the solution set, which is the case for inequalities using < or >.

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What does a solid line represent in a graph of an inequality?

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A solid line indicates that the points on the line are included in the solution set, which is the case for inequalities using ≤ or ≥.

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How can you tell which side of the line to shade in a graph of an inequality?

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To determine which side to shade, pick a test point not on the line (often (0,0) is used) and substitute it into the inequality. If the inequality holds true, shade that side.