Solutions to Systems of Inequalities- Graphs!

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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 graph a linear inequality?

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To graph a linear inequality, first graph the corresponding equation as a line. Use a solid line for '≥' or '≤' and a dashed line for '>' or '<'. 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 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 shaded region in a graph of inequalities?

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The shaded region represents all possible solutions to the inequality. Any point within this region is a solution.

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 the intersection of two shaded regions represent?

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The intersection of two shaded regions represents the set of solutions that satisfy both inequalities in the system.

Tags

CCSS.HSA.REI.D.12

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What is a boundary line in the context of inequalities?

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A boundary line is the line that represents the equation of the inequality. It divides the graph into two regions: one that satisfies the inequality and one that does not.

Tags

CCSS.HSA.REI.D.12

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How do you solve a system of 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 intersection of the shaded areas.

Tags

CCSS.HSA.REI.D.12

Front

What is the solution set of a system of inequalities?

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The solution set is the collection of all points that satisfy all inequalities in the system, often represented as a shaded region on a graph.

Tags

CCSS.HSA.REI.D.12