System 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 boundary line. Use a dashed line for < or > and a solid line for ≤ or ≥. Then, shade the region that satisfies the inequality.

Tags

CCSS.HSA.REI.D.12

Front

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

Front

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

Front

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

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What is the graphical representation of the inequality y > 2x - 4?

Back

The graphical representation is a dashed line for y = 2x - 4, with the region above the line shaded.

Tags

CCSS.HSA.REI.D.12

Front

What does the inequality y ≤ 2x - 1 represent graphically?

Back

It represents a solid line for y = 2x - 1, with the region below the line shaded.

Tags

CCSS.HSA.REI.D.12

Front

What is the solution set of the system of inequalities y < 2 and y > -2x + 3?

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The solution set is the region where the area below the line y = 2 and above the line y = -2x + 3 overlap.

Tags

CCSS.HSA.REI.D.12

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

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A point that does not satisfy at least one of the inequalities in the system is not a solution.

Front

What is the significance of the intersection of shaded regions in a system of inequalities?

Back

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

Tags

CCSS.HSA.REI.D.12