Systems of Inequalities review

Front

What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities with the same variables. The solution is the set of all points that satisfy all inequalities in the system.

Tags

CCSS.HSA.REI.D.12

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a solid line (for ≤ or ≥) or a dashed line (for < or >). Then, shade the region that satisfies the inequality.

Tags

CCSS.HSA.REI.D.12

Front

What does it mean when a point is a solution to a system of inequalities?

Back

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 happens to the inequality symbol when you multiply or divide by a negative number?

Back

The inequality symbol flips direction when you multiply or divide both sides of an inequality by a negative number.

Tags

CCSS.6.EE.B.8

Front

Back

Tags

CCSS.HSA.REI.D.12

Front

How do you determine if a point is a solution to an inequality?

Back

To determine if a point is a solution to an inequality, substitute the x and y values of the point into the inequality. If the inequality holds true, the point is a solution.

Front

What is the difference between a solid line and a dashed line in graphing inequalities?

Back

A solid line indicates that points on the line are included in the solution (for ≤ or ≥), while a dashed line indicates that points on the line are not included (for < or >).

Tags

CCSS.HSA.REI.D.12

Front

Back

Tags

CCSS.HSA.REI.D.12

Front

How can you find the intersection of two inequalities?

Back

To find the intersection of two inequalities, graph both inequalities and identify the region where the shaded areas overlap. This overlapping region represents the solution to the system.

Tags

CCSS.HSA.REI.D.12

Front

What does it mean for a point to be 'not a solution' to a system of inequalities?

Back

A point is 'not a solution' if it does not satisfy at least one of the inequalities in the system, meaning it lies outside the shaded region.

Tags

CCSS.HSA.REI.D.12