System 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 set of all points that satisfy all inequalities in the system.

Front

What does a dashed line indicate in a graph of an inequality?

Back

A dashed line indicates that the points on the line are not included in the solution set of the inequality.

Front

What does a solid line indicate in a graph of an inequality?

Back

A solid line indicates that the points on the line are included in the solution set of the inequality.

Front

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

Back

To determine if a point is a solution, substitute the point's coordinates into each inequality. If the point satisfies all inequalities, it is a solution.

Front

What is the graphical representation of the inequality y < 2?

Back

The graphical representation is a horizontal dashed line at y = 2, with the area below the line shaded.

Front

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

Back

The graphical representation is a solid line for y = 2x - 4, with the area above the line shaded.

Front

What does the inequality y < 2x - 4 represent?

Back

It represents all points below the line y = 2x - 4, excluding the line itself.

Front

What is the solution set of the system y > 2x - 4 and y < 2?

Back

The solution set includes all points above the line y = 2x - 4 and below the line y = 2.

Front

How do you graph the system of inequalities y ≥ -x - 1 and y < x + 4?

Back

Graph the solid line for y = -x - 1 and shade above it. Then graph the dashed line for y = x + 4 and shade below it.

Front

What is the significance of the intersection of shaded regions in a system of inequalities?

Back

The intersection of shaded regions represents the solution set where all inequalities are satisfied.