Graphing systems of Inequalities

Front

What is a system of inequalities?

Back

A set of two or more inequalities with the same variables. Solutions are the values that satisfy all inequalities in the system.

Front

How do you graph a linear inequality?

Back

1. Graph the boundary line (dashed for < or >, solid for ≤ or ≥). 2. Choose a test point not on the line to determine which side to shade.

Tags

CCSS.HSA.REI.D.12

Front

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

Back

It means that the point satisfies all inequalities in the system.

Front

What is the difference between '>' and '≥'?

Back

'>' means the value is greater than, while '≥' means the value is greater than or equal to.

Tags

CCSS.6.EE.B.8

Front

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

Back

Substitute the point's coordinates into each inequality. If it satisfies all, it is a solution.

Front

What is the graphical representation of y > mx + b?

Back

The area above the line y = mx + b is shaded, indicating all points where y is greater than the line.

Tags

CCSS.HSA.REI.D.12

Front

What does the solution set of a system of inequalities represent?

Back

It represents all the points that satisfy all inequalities in the system, often shown as a shaded region on a graph.

Tags

CCSS.HSA.REI.D.12

Front

What is the significance of the boundary line in graphing inequalities?

Back

The boundary line separates the solution set from the non-solution set. It can be solid or dashed depending on the inequality.

Tags

CCSS.HSA.REI.D.12

Front

How do you solve a system of inequalities by graphing?

Back

Graph each inequality on the same coordinate plane and identify the overlapping shaded region as the solution.

Tags

CCSS.HSA.REI.D.12

Front

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

Back

It means there is no point that satisfies all inequalities, often represented by parallel lines that never intersect.

Tags

CCSS.HSA.REI.D.12