Solving & Graphing Systems of Inequalities

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that compares a linear expression to a value using inequality symbols such as <, >, ≤, or ≥.

Front

What does the graph of a linear inequality represent?

Back

The graph of a linear inequality represents all the solutions that satisfy the inequality, typically shown as a shaded region on a coordinate plane.

Tags

CCSS.HSA.REI.D.12

Front

What is the slope-intercept form of a linear equation?

Back

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

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

Back

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

Front

What does the symbol '≤' mean in a linear inequality?

Back

The symbol '≤' means 'less than or equal to', indicating that the values can be equal to the boundary line or less than it.

Tags

CCSS.HSA.REI.D.12

Front

What does the symbol '≥' mean in a linear inequality?

Back

The symbol '≥' means 'greater than or equal to', indicating that the values can be equal to the boundary line or greater than it.

Tags

CCSS.HSA.REI.D.12

Front

What is the significance of a dashed line in the graph of a linear inequality?

Back

A dashed line indicates that the points on the line are not included in the solution set, representing strict inequalities (< or >).

Tags

CCSS.HSA.REI.D.12

Front

What is the significance of a solid line in the graph of a linear inequality?

Back

A solid line indicates that the points on the line are included in the solution set, representing inclusive inequalities (≤ or ≥).

Tags

CCSS.HSA.REI.D.12

Front

How do you graph a system of inequalities?

Back

To graph a system of inequalities, graph each inequality on the same coordinate plane and identify the overlapping shaded region, which represents the solution set.

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 where the shaded areas of all inequalities overlap on the graph.

Tags

CCSS.HSA.REI.D.12