Solving Systems of Inequalities

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What is a system of inequalities?

Back

A set of two or more inequalities with the same variables.

Tags

CCSS.8.EE.C.8B

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How do you represent a system of inequalities graphically?

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By shading the regions that satisfy all inequalities in the system.

Tags

CCSS.HSA.REI.D.12

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What does a dashed line indicate in graphing inequalities?

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It indicates that the points on the line are not included in the solution (for < or > inequalities).

Tags

CCSS.HSA.REI.D.12

Front

What does a solid line indicate in graphing inequalities?

Back

It indicates that the points on the line are included in the solution (for ≤ or ≥ inequalities).

Tags

CCSS.HSA.REI.D.12

Front

What is the solution to a system of inequalities?

Back

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

Tags

CCSS.HSA.REI.D.12

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If a system of inequalities has no overlapping shaded regions, what does that mean?

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It means there is no solution to the system.

Tags

CCSS.HSA.REI.D.12

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What is the significance of the boundary line in a system of inequalities?

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It separates the solution region from the non-solution region.

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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Substitute the point into each inequality; if it satisfies all, 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 (< or >) does not include the boundary, while a non-strict inequality (≤ or ≥) does.

Tags

CCSS.6.EE.B.8

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Can a system of inequalities have infinitely many solutions?

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Yes, if the shaded regions overlap, there can be infinitely many solutions.

Tags

CCSS.HSA.REI.D.12