Systems of Linear Inequalities

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What is a system of linear inequalities?

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A system of linear 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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CCSS.8.EE.C.8B

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What does it mean for a point to be part of the solution set of a system of linear inequalities?

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A point is part of the solution set if it satisfies all the inequalities in the system.

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CCSS.HSA.REI.D.12

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What is the significance of boundary lines in linear inequalities?

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Boundary lines represent the limits of the solution set. Points on the boundary line may or may not be included in the solution set, depending on whether the inequality is strict (>) or non-strict (≥).

Tags

CCSS.HSA.REI.D.12

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How do you determine if a point is a solution to a system of linear 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 is the difference between a strict inequality and a non-strict inequality?

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A strict inequality (e.g., < or >) does not include the boundary line, while a non-strict inequality (e.g., ≤ or ≥) includes the boundary line.

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CCSS.6.EE.B.8

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What does the graph of a system of linear inequalities look like?

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The graph consists of shaded regions representing the solution sets of the inequalities, along with boundary lines that may be solid or dashed.

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CCSS.HSA.REI.D.12

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What does it mean if a boundary line is dashed in a graph of linear inequalities?

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A dashed boundary line indicates that points on the line are not included in the solution set (strict inequality).

Tags

CCSS.HSA.REI.D.12

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What does it mean if a boundary line is solid in a graph of linear inequalities?

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A solid boundary line indicates that points on the line are included in the solution set (non-strict inequality).

Tags

CCSS.HSA.REI.D.12

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How can you find the solution set of a system of linear inequalities graphically?

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To find the solution set graphically, graph each inequality, shade the appropriate region, and identify the overlapping shaded area as the solution set.

Tags

CCSS.HSA.REI.D.12

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What is the role of test points in solving linear inequalities?

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

Tags

CCSS.HSA.REI.D.12