Graphing Systems of Inequalities and Equations

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What is a system of inequalities?

Back

A set of two or more inequalities with the same variables.

Tags

CCSS.8.EE.C.8B

Front

What does it mean if a system of inequalities has no solution?

Back

It means that the graphs of the inequalities do not intersect at any point.

Tags

CCSS.HSA.REI.D.12

Front

What does it mean if a system of inequalities has infinitely many solutions?

Back

It means that the graphs of the inequalities overlap completely.

Tags

CCSS.HSA.REI.D.12

Front

What is the graphical representation of a linear inequality?

Back

A shaded region on one side of a boundary line.

Tags

CCSS.HSA.REI.D.12

Front

How do you determine if a point is a solution to a system of inequalities?

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Substitute the point into each inequality; if it satisfies all, it is a solution.

Front

What does it mean if two lines are parallel in a system of equations?

Back

They have the same slope and will never intersect, resulting in no solutions.

Tags

CCSS.8.EE.C.8A

Front

What does it mean if two lines are the same in a system of equations?

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They have the same slope and y-intercept, resulting in infinitely many solutions.

Tags

CCSS.8.EE.C.8A

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What is the significance of the intersection point of two lines in a system of equations?

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It represents the unique solution to the system.

Tags

CCSS.8.EE.C.8A

Front

How can you graph a system of inequalities?

Back

Graph each inequality as a line, then shade the appropriate region for each.

Tags

CCSS.HSA.REI.D.12

Front

What is the difference between a solution to an equation and a solution to an inequality?

Back

An equation has specific solutions, while an inequality has a range of solutions.