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.

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.

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 >).

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 ≥).

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.

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.

Front

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

Back

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

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.