Graphing Systems of Inequalities Flashcard Review

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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 set of all points that satisfy all inequalities in the system.

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How do you graph a linear inequality?

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To graph a linear inequality, first graph the corresponding linear equation as a dashed or solid line (depending on whether the inequality is strict or inclusive). Then, shade the region that satisfies the inequality.

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What does it mean for a point to be a solution to a system of inequalities?

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A point is a solution to a system of inequalities if it satisfies all inequalities in the system, meaning it lies in the shaded region of the graph.

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What is the difference between '<' and '≤' in inequalities?

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The symbol '<' indicates that the value is strictly less than, while '≤' indicates that the value can be less than or equal to.

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What is the significance of the overlap in shaded regions when graphing systems of inequalities?

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The overlap in shaded regions represents the set of solutions that satisfy all inequalities in the system.

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How do you determine if a point is in the solution set of a system of inequalities?

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To determine if a point is in the solution set, substitute the point's coordinates into each inequality. If the point satisfies all inequalities, it is 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 value on the left is greater than the value on the right, excluding equality.

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What is the purpose of shading in the graph of an inequality?

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Shading indicates the set of all points that satisfy the inequality. The shaded area represents the solution set.

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How do you identify the solution set of a system of inequalities graphically?

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The solution set is identified by the region where the shaded areas of all inequalities overlap.