Graphing 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 graph a linear inequality?

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To graph a linear inequality, first graph the corresponding equation as a line. Use a dashed line for < or > and a solid line for ≤ or ≥. 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 the inequalities in the system.

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

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

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How can 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 is the solution set of a system of inequalities?

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The solution set is the collection of all points that satisfy all inequalities in the system, often represented as a shaded region on a graph.

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What is the significance of the intersection of two inequalities?

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The intersection of two inequalities represents the set of points that satisfy both inequalities simultaneously, forming the solution region.

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How do you find the boundary lines for a system of inequalities?

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To find the boundary lines, convert each inequality into an equation (replace <, >, ≤, or ≥ with =) and graph these lines.

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What is the role of test points in graphing inequalities?

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Test points are used to determine which side of the boundary line to shade. If the test point satisfies the inequality, shade that side.