Systems of Inequalities

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 in two variables?

Back

To graph a linear inequality, first graph the corresponding linear equation as a dashed or solid line. Then, shade the appropriate half-plane based on the inequality symbol.

Tags

CCSS.HSA.REI.D.12

Front

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

Back

A dashed line indicates that the points on the line are not included in the solution set (i.e., the inequality is strict, such as < 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 (i.e., the inequality is non-strict, such as ≤ or ≥).

Tags

CCSS.HSA.REI.D.12

Front

What is the solution set of a system of inequalities?

Back

The solution set of a system of inequalities is the region on the graph where the shaded areas of all inequalities overlap.

Tags

CCSS.HSA.REI.D.12

Front

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

Back

To determine if a point is a solution, substitute the point's coordinates into each inequality. If the point satisfies all inequalities, it is part of the solution set.

Front

What is the significance of the boundary line in a linear inequality?

Back

The boundary line separates the coordinate plane into two half-planes, one of which contains the solutions to the inequality.

Tags

CCSS.HSA.REI.D.12

Front

What does the term 'half-plane' refer to in the context of inequalities?

Back

A half-plane refers to one of the two regions created by a boundary line in the graph of a linear inequality, where all points satisfy the inequality.

Tags

CCSS.HSA.REI.D.12

Front

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

Back

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

Tags

CCSS.6.EE.B.8

Front

How do you identify a point that is NOT part of the solution set?

Back

A point that does not satisfy at least one of the inequalities in the system is NOT part of the solution set.

Tags

CCSS.HSA.REI.D.12