Graphing Systems of Linear Inequalities

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that relates a linear expression to a value using inequality symbols (>, <, ≥, ≤). It represents a region of the coordinate plane.

Front

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

Back

The solution set represents all the points that satisfy all inequalities in the system, typically shown as a shaded region on a graph.

Tags

CCSS.HSA.REI.D.12

Front

How do you graph a linear inequality?

Back

1. Graph the corresponding linear equation as a boundary line. 2. Use a dashed line for < or > and a solid line for ≤ or ≥. 3. Shade the region that satisfies the inequality.

Tags

CCSS.HSA.REI.D.12

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

Tags

CCSS.HSA.REI.D.12

Front

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

Back

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

Tags

CCSS.HSA.REI.D.12

Front

What does it mean if a system of inequalities has an infinite number of solutions?

Back

It means that there are infinitely many points that satisfy all inequalities, often represented by overlapping shaded regions.

Tags

CCSS.HSA.REI.D.12

Front

How can you determine if a point is part of the solution set for a system of inequalities?

Back

Substitute the coordinates of the point into each inequality. If the point satisfies all inequalities, it is part of the solution set.

Front

Back

Tags

CCSS.HSA.REI.D.12

Front

What is the significance of the intersection of two inequalities in a system?

Back

The intersection represents the set of points that satisfy both inequalities, which is the solution set for the system.

Tags

CCSS.HSA.REI.D.12

Front

How do you solve a system of inequalities by graphing?

Back

1. Graph each inequality on the same coordinate plane. 2. Identify the overlapping shaded region. 3. This region represents the solution set.

Tags

CCSS.HSA.REI.D.12