Systems of Inequalities

Front

What is a system of inequalities?

Back

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

Front

What does a solid line represent in graphing inequalities?

Back

A solid line indicates that the points on the line are included in the solution set (i.e., the inequality is '≤' or '≥').

Front

What does a dashed line represent in graphing inequalities?

Back

A dashed line indicates that the points on the line are not included in the solution set (i.e., the inequality is '<' or '>').

Front

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

Back

Substitute the coordinates of the point into the inequality. If the inequality holds true, then the point is a solution.

Front

What is the significance of the shaded region in a graph of inequalities?

Back

The shaded region represents all the possible solutions to the inequality.

Front

What does the inequality 5 ≥ x mean in terms of graphing?

Back

It means that the graph will include all points to the left of and including the vertical line at x = 5.

Front

How can you tell if a point lies in the solution set of a system of inequalities?

Back

If the point satisfies all inequalities in the system, it lies in the solution set.

Front

What is the solution set of the inequality 2x - 3y < 5?

Back

The solution set includes all points below the dashed line represented by the equation 2x - 3y = 5.

Front

What does it mean if a point is on a dashed line in a graph of an inequality?

Back

It means that the point is not included in the solution set of the inequality.

Front

What is the first step in graphing a system of inequalities?

Back

The first step is to graph each inequality on the same coordinate plane.