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

Tags

CCSS.HSA.REI.D.12

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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 it mean if a point is a solution to a system of inequalities?

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It means that the point lies in the region where all inequalities overlap, representing the solution set.

Tags

CCSS.HSA.REI.D.12

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What is the graphical representation of a linear inequality?

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The graphical representation of a linear inequality is a half-plane divided by a boundary line, which can be solid (inclusive) or dashed (exclusive).

Tags

CCSS.HSA.REI.D.12

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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 <).

Tags

CCSS.HSA.REI.D.12

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Tags

CCSS.HSA.REI.D.12

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

Tags

CCSS.HSA.REI.D.12

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How do you find the intersection of two inequalities?

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To find the intersection, graph both inequalities and identify the region where their shaded areas overlap.

Tags

CCSS.HSA.REI.D.12

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What does the term 'feasible region' refer to in the context of systems of inequalities?

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The feasible region is the area on the graph that satisfies all inequalities in the system, representing all possible solutions.

Tags

CCSS.HSA.REI.D.12

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What is the significance of the vertices in the feasible region?

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The vertices of the feasible region are potential solutions to the system of inequalities and can be evaluated to find optimal solutions in linear programming.