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

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A point is part of the solution set if it satisfies 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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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 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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What does the inequality y ≥ -x - 1 represent graphically?

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It represents the region above and including the line y = -x - 1.

Tags

CCSS.HSA.REI.D.12

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What does the inequality y < x + 4 represent graphically?

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It represents the region below the line y = x + 4, not including the line itself.

Tags

CCSS.HSA.REI.D.12

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What is the significance of the solution set in a system of inequalities?

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The solution set represents all possible solutions that satisfy all inequalities in the system.

Tags

CCSS.HSA.REI.D.12

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Can a system of inequalities have no solution?

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Yes, if the inequalities represent parallel lines that do not intersect, there is no solution.

Tags

CCSS.HSA.REI.D.12

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What does it mean if a system of inequalities has an infinite number of solutions?

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It means that there are countless points that satisfy all inequalities, often occurring when the inequalities overlap significantly.

Tags

CCSS.HSA.REI.D.12

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How do you graph a system of inequalities?

Back

Graph each inequality on the same coordinate plane, shading the appropriate regions that satisfy each inequality.

Tags

CCSS.HSA.REI.D.12