Systems of Inequalities Practice

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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 system of inequalities has no solution?

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A system of inequalities has no solution if there are no points that satisfy all inequalities simultaneously, often resulting in parallel lines that never intersect.

Tags

CCSS.HSA.REI.D.12

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What does it mean if a system of inequalities has an infinite number of solutions?

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A system of inequalities has an infinite number of solutions if the inequalities 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 graphical representation of a system of inequalities?

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The graphical representation consists of shaded regions on a coordinate plane, where each region corresponds to the solutions of the inequalities.

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 equation as a line. Use a dashed line for < or > and a solid line for ≤ or ≥. Then shade the appropriate region.

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 (≤ 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 the solution set of a system of inequalities represent?

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The solution set represents all the points (x, y) that satisfy all inequalities in the system, shown as the overlapping shaded regions on the graph.

Tags

CCSS.HSA.REI.D.12

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How can you solve a system of inequalities by graphing?

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To solve by graphing, graph each inequality on the same coordinate plane, identify the overlapping shaded region, which represents the solution set.

Tags

CCSS.HSA.REI.D.12

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What is the significance of the intersection of two inequalities?

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The intersection of two inequalities represents the set of points that satisfy both inequalities simultaneously, forming the solution set.

Tags

CCSS.HSA.REI.D.12