Graphing 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 that share 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 system of inequalities?

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To graph a system of inequalities, first graph each inequality as if it were an equation. Use a dashed line for inequalities that do not include equality (e.g., < or >) and a solid line for those that do (e.g., ≤ or ≥). Then, shade the appropriate region for each inequality, and the solution set is where the shaded regions overlap.

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. This means that when the coordinates of the point are substituted into each inequality, the resulting statements are true.

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

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What is the significance of the boundary line in graphing inequalities?

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The boundary line represents the points where the inequality changes from true to false. For a solid line, points on the line are included in the solution (≤ or ≥), while for a dashed line, they are not included (< or >).

Tags

CCSS.HSA.REI.D.12

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What does the notation y < -1/5x - 1/2 represent?

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This notation represents an inequality where the y-values are less than the values given by the linear equation -1/5x - 1/2. The area below this line is shaded when graphed.

Tags

CCSS.HSA.REI.D.12

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What is the difference between a solution and a non-solution in the context of inequalities?

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A solution satisfies all inequalities in the system, while a non-solution does not satisfy at least one inequality.

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What does it mean if a point is 'not a solution' to a system of inequalities?

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If a point is 'not a solution,' it means that when the coordinates of the point are substituted into the inequalities, at least one of the inequalities is false.

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How do you identify a point that is NOT a solution to a system of inequalities?

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To identify a point that is NOT a solution, substitute the point's coordinates into each inequality. If any inequality is not satisfied, then that point is not a solution.

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What is the graphical representation of the solution set for a system of inequalities?

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The graphical representation of the solution set is the region where the shaded areas of all inequalities overlap on the graph.

Tags

CCSS.HSA.REI.D.12