Identify Solutions to Systems of Inequalities

Front

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

Front

What does it mean if a line is dashed in a graph of an inequality?

Back

A dashed line indicates that the points on the line are not included in the solution set of the inequality.

Tags

CCSS.HSA.REI.D.12

Front

What does it mean if a line is solid in a graph of an inequality?

Back

A solid line indicates that the points on the line are included in the solution set of the inequality.

Tags

CCSS.HSA.REI.D.12

Front

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

Back

A point is a solution if it satisfies all inequalities in the system, meaning it lies in the common shaded region of the graph.

Tags

CCSS.HSA.REI.D.12

Front

What is the common shaded region in a graph of inequalities?

Back

The common shaded region is the area where the shaded regions of all inequalities overlap, representing the solution set of the system.

Tags

CCSS.HSA.REI.D.12

Front

Back

Tags

CCSS.HSA.REI.D.12

Front

Back

Tags

CCSS.HSA.REI.D.12

Front

How can you tell if a point is in the unshaded region of a graph?

Back

A point is in the unshaded region if it does not satisfy any of the inequalities in the system, meaning it lies outside the common shaded region.

Tags

CCSS.HSA.REI.D.12

Front

What is the significance of the ordered pair (1, 2) in relation to a system of inequalities?

Back

The ordered pair (1, 2) is not a solution if it lies on a dashed line or outside the common shaded region of the graph.

Tags

CCSS.HSA.REI.D.12

Front

What does it mean if a point is a solution for only one inequality in a system?

Back

It means that the point satisfies one inequality but does not satisfy the other(s), indicating it is not part of the solution set for the entire system.

Tags

CCSS.HSA.REI.D.12