Solving Systems of Linear Inequalities

Front

What is a system of linear inequalities?

Back

A system of linear inequalities is a set of two or more inequalities with the same variables. The solution is the region where the graphs of the inequalities overlap.

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 dashed or solid line, then shade the region that satisfies the inequality.

Tags

CCSS.HSA.REI.D.12

Front

What does a dashed line indicate in graphing inequalities?

Back

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

Tags

CCSS.HSA.REI.D.12

Front

What does a solid line indicate in graphing inequalities?

Back

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

Tags

CCSS.HSA.REI.D.12

Front

What is the solution to the inequality y > 2?

Back

The solution is the region above the horizontal line y = 2, not including the line itself.

Tags

CCSS.HSA.REI.D.12

Front

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

Back

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

Front

What is the significance of the intersection of two inequalities?

Back

The intersection represents the set of solutions that satisfy both inequalities simultaneously.

Tags

CCSS.HSA.REI.D.12

Front

What does the inequality y ≤ -x + 3 represent graphically?

Back

It represents the region below and including the line y = -x + 3.

Tags

CCSS.HSA.REI.D.12

Front

How can you tell if a point (x, y) is a solution to the inequality y < 3x - 1?

Back

Substitute x and y into the inequality. If the resulting statement is true, then (x, y) is a solution.

Front

What is the graphical representation of the inequality y ≥ 2x - 4?

Back

It includes the area above the line y = 2x - 4, including the line itself.

Tags

CCSS.HSA.REI.D.12