Graphing Systems of Inequalities

Front

What is a system of inequalities?

Back

A set of two or more inequalities with the same variables.

Front

How do you graph a system of inequalities?

Back

1. Graph each inequality on the same coordinate plane. 2. Use a dashed line for < or > and a solid line for ≤ or ≥. 3. Shade the appropriate region for each inequality. 4. The solution set is where the shaded regions overlap.

Front

What does the inequality x > -2 represent on a graph?

Back

A vertical line at x = -2, with the area to the right shaded.

Front

What does the inequality y < -4 represent on a graph?

Back

A horizontal line at y = -4, with the area below shaded.

Front

What is the solution to the system: x > 2 and y < -4?

Back

The region above the line x = 2 and below the line y = -4.

Front

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

Back

Substitute the point's coordinates into each inequality. If all inequalities are satisfied, the point is a solution.

Front

What does the notation y ≤ 3x mean?

Back

The line y = 3x is included in the solution set, and the area below the line is shaded.

Front

What is the significance of a dashed line in graphing inequalities?

Back

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

Front

What does the inequality y > -2x + 4 represent?

Back

A line with a slope of -2 and a y-intercept of 4, with the area above the line shaded.

Front

What is the solution set of the inequalities y ≤ 3x and y ≤ -2x + 4?

Back

The region where both shaded areas from the inequalities overlap.