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 linear inequalities that involve the same variables. The solution is the set of all points that satisfy all inequalities in the system.

Tags

CCSS.8.EE.C.8B

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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 (solid for ≤ or ≥, dashed for < or >). Then, shade the region that satisfies the inequality.

Tags

CCSS.HSA.REI.D.12

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What does it mean if a point is 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 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 (for ≤ or ≥), while a dashed line indicates that points on the line are not included (for < or >).

Tags

CCSS.HSA.REI.D.12

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What is the solution set of a system of linear inequalities?

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The solution set is the region on the graph where all inequalities overlap, representing all possible solutions that satisfy the system.

Tags

CCSS.HSA.REI.D.12

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How can 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 for a system of inequalities to have no solution?

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A system of inequalities has no solution if the shaded regions of the inequalities do not overlap, meaning there are no points that satisfy all inequalities.

Tags

CCSS.HSA.REI.D.12

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What does it mean for a system of inequalities to have infinitely many solutions?

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A system of inequalities has infinitely many solutions if the shaded regions overlap in such a way that there are countless points that satisfy all inequalities.

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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The boundary line separates the solution region from the non-solution region. It helps to visually identify where the solutions to the inequalities lie.

Tags

CCSS.HSA.REI.D.12

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How do you solve a system of linear inequalities by graphing?

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To solve by graphing, graph each inequality on the same coordinate plane, shade the appropriate regions, and identify the overlapping shaded area as the solution.

Tags

CCSS.HSA.REI.D.12