Systems 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 are considered simultaneously. 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 represent a linear inequality graphically?

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A linear inequality is represented graphically by a region on a coordinate plane, which is bounded by a line. The line can be solid (for ≤ or ≥) or dotted (for < or >).

Tags

CCSS.HSA.REI.D.12

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What does a dotted line indicate in the graph of an inequality?

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A dotted line indicates that the points on the line are not included in the solution set, which is the case for inequalities using < or >.

Tags

CCSS.HSA.REI.D.12

Front

What does a solid line indicate in the graph of an inequality?

Back

A solid line indicates that the points on the line are included in the solution set, which is the case for inequalities using ≤ or ≥.

Tags

CCSS.HSA.REI.D.12

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How do you determine the solution set of a system of linear inequalities?

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The solution set is determined by finding the intersection of the regions represented by each inequality in the system.

Tags

CCSS.HSA.REI.D.12

Front

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, which is the solution to the system.

Tags

CCSS.HSA.REI.D.12

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

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The graphical representation is a region above the line y = 2x - 4, with a dotted line indicating that points on the line are not included.

Tags

CCSS.HSA.REI.D.12

Front

What is the graphical representation of the inequality y ≤ 2x - 1?

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The graphical representation is a region below and including the line y = 2x - 1, with a solid line indicating that points on the line are included.

Tags

CCSS.HSA.REI.D.12

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Can a system of linear inequalities have no solution?

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Yes, a system of linear inequalities can have no solution if the regions represented by the inequalities do not overlap.

Tags

CCSS.HSA.REI.D.12

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

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It means that there are infinitely many points that satisfy all inequalities in the system, often occurring when the inequalities represent the same line or overlapping regions.

Tags

CCSS.HSA.REI.D.12