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 coordinates of the point 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 above the line in a graph of an inequality?

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If a point is above the line in a graph of an inequality, it means that the point satisfies the inequality, indicating that it is a solution.

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What does it mean if a point is below the line in a graph of an inequality?

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If a point is below the line in a graph of an inequality, it means that the point does not satisfy the inequality, indicating that it is not a solution.

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

Tags

CCSS.HSA.REI.D.12

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How do you graph the inequality y > -2x + 1?

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1. Graph the line y = -2x + 1 with a dashed line. 2. Shade the area above the line to represent all points where y is greater than -2x + 1.

Tags

CCSS.HSA.REI.D.12

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How do you graph the inequality y ≤ x + 3?

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1. Graph the line y = x + 3 with a solid line. 2. Shade the area below the line to represent all points where y is less than or equal to x + 3.

Tags

CCSS.HSA.REI.D.12

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What is the solution region for a system of inequalities?

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The solution region is the area where the shaded regions of all inequalities overlap. This area contains all the points that satisfy all inequalities in the system.

Tags

CCSS.HSA.REI.D.12

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What does it mean if a point is a vertex of the solution region?

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A vertex of the solution region is a corner point where two or more boundary lines intersect. It is often a candidate for the optimal solution in linear programming.

Tags

CCSS.HSA.REI.D.12

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How can you find a solution to a system of inequalities?

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To find a solution, graph each inequality, identify the overlapping shaded region, and select any point within that region.

Tags

CCSS.HSA.REI.D.12