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 with 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 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 x and y values of the point into each inequality. If the point satisfies all inequalities, it is a solution.

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What does the graph of a linear inequality represent?

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The graph of a linear inequality represents all the solutions to that inequality, typically shaded on one side of the boundary line.

Tags

CCSS.HSA.REI.D.12

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What is the difference between '>' and '≥' in inequalities?

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'>' means that the value is strictly greater than, while '≥' means that the value is greater than or equal to.

Tags

CCSS.6.EE.B.8

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What is the significance of the boundary line in a linear inequality?

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The boundary line represents the points where the inequality changes from true to false. It is solid for '≥' or '≤' and dashed for '>' or '<'.

Tags

CCSS.HSA.REI.D.12

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How do you graph a system of linear inequalities?

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1. Graph each inequality as if it were an equation. 2. Use a solid line for '≥' or '≤' and a dashed line for '>' or '<'. 3. Shade the appropriate region for each inequality. 4. The solution is where the shaded regions overlap.

Tags

CCSS.HSA.REI.D.12

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What does it mean if a point lies on the boundary line of an inequality?

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If a point lies on the boundary line of an inequality, it is a solution if the inequality includes equality (≥ or ≤). If the inequality is strict (> or <), the point is not a solution.

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 the shaded areas of all inequalities overlap, representing all possible solutions.

Tags

CCSS.HSA.REI.D.12

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How can you tell if a point is not a solution to a system of inequalities?

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A point is not a solution if it does not satisfy at least one of the inequalities when substituted into them.

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What is the role of test points in solving systems of inequalities?

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Test points are used to determine which side of the boundary line to shade. If the test point satisfies the inequality, shade the region containing that point.

Tags

CCSS.HSA.REI.D.12