Solving 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 that involve 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 graph a linear inequality?

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To graph a linear inequality, first graph the corresponding linear equation as a dashed or solid line, depending on whether the inequality is strict (<, >) or inclusive (≤, ≥). Then, shade the region that satisfies the inequality.

Tags

CCSS.HSA.REI.D.12

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

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A point is a solution to a system of inequalities if it satisfies all inequalities in the system, meaning it lies in the shaded region of the graph.

Tags

CCSS.HSA.REI.D.12

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What is the significance of the shaded area in the graph of a system of inequalities?

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The shaded area represents all possible solutions to the system of inequalities. Points within this area satisfy all inequalities.

Tags

CCSS.HSA.REI.D.12

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What does it mean if two inequalities have no overlapping shaded region?

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If two inequalities have no overlapping shaded region, it means that there are no solutions that satisfy both inequalities simultaneously.

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 is the difference between a solid line and a dashed line in the graph of 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 it mean for a system of inequalities to be consistent?

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A system of inequalities is consistent if there is at least one solution that satisfies all inequalities in the system.

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What is an example of a system of linear inequalities?

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An example is: y < 2x + 3 and y ≥ -x - 1.

Tags

CCSS.8.EE.C.8B

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

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

Tags

CCSS.HSA.REI.D.12