systems of inequalities

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What is a system of inequalities?

Back

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 represent a solution set graphically for a system of inequalities?

Back

The solution set is represented by the overlapping region of the graphs of the inequalities.

Tags

CCSS.HSA.REI.D.12

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What does a dotted line indicate when graphing an inequality?

Back

A dotted line indicates that the points on the line are not included in the solution set, used for inequalities with < or >.

Tags

CCSS.HSA.REI.D.12

Front

What does a solid line indicate when graphing an inequality?

Back

A solid line indicates that the points on the line are included in the solution set, used for inequalities with ≤ or ≥.

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?

Back

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

Front

What is the significance of the boundary lines in a system of inequalities?

Back

Boundary lines separate the graph into regions, and the solution set is found in the region that satisfies all inequalities.

Tags

CCSS.HSA.REI.D.12

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What is the difference between a strict inequality and a non-strict inequality?

Back

A strict inequality (< or >) does not include the boundary, while a non-strict inequality (≤ or ≥) includes the boundary.

Tags

CCSS.6.EE.B.8

Front

How do you graph the inequality y ≤ (1/2)x + 2?

Back

Graph the line y = (1/2)x + 2 with a solid line, then shade below the line to represent y values that are less than or equal to the line.

Tags

CCSS.HSA.REI.D.12

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What is the solution set for the system of inequalities y ≤ (1/2)x + 2 and -y > -3x - 1?

Back

The solution set is the region where the shaded areas of both inequalities overlap.

Tags

CCSS.HSA.REI.D.12

Front

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

Back

It means that the point does not satisfy at least one of the inequalities in the system.