Systems of Inequalities

Front

What is a system of inequalities?

Back

A set of two or more inequalities with the same variables that are solved together.

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 (≥ 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 (> or <).

Front

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

Back

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

Front

What is the graphical representation of the inequality y > -x - 1?

Back

The area above the line y = -x - 1, not including the line itself.

Front

What is the graphical representation of the inequality y ≤ x + 3?

Back

The area below the line y = x + 3, including the line itself.

Front

How do you graph the system of inequalities y > -2x + 1 and y ≤ x + 3?

Back

Graph both lines, use a dashed line for y > -2x + 1 and a solid line for y ≤ x + 3, then shade the appropriate regions.

Front

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

Back

Graph each inequality on the same coordinate plane.

Front

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

Back

The region where the shaded areas of all inequalities overlap.

Front

In the context of a movie theater, what does the inequality x + y ≤ 300 represent?

Back

The total number of adult (x) and child (y) tickets sold cannot exceed the number of seats.