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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What does the symbol '<' indicate in an inequality?

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The symbol '<' indicates that the line is dotted, meaning that points on the line are not included in the solution set.

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What does the symbol '≤' indicate in an inequality?

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The symbol '≤' indicates that the line is solid, meaning that points on the line are included in the solution set.

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The solution is the region where the shaded areas of both inequalities overlap on the graph.

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What is the difference between a solid line and a dotted line in graphing inequalities?

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A solid line indicates that points on the line are included in the solution (for '≤' or '≥'), while a dotted line indicates that points on the line are not included (for '<' or '>').

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

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Substitute the coordinates of the point into each inequality. If the point satisfies all inequalities, it is a solution.

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What does the intersection of two inequalities represent?

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The intersection represents the set of all points that satisfy both inequalities simultaneously.

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