Systems of Inequalities

Front

What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities that share the same variables. The solution is the set of all points that satisfy all inequalities in the system.

Front

How do you graph a system of inequalities?

Back

To graph a system of inequalities, first graph each inequality as if it were an equation. Use a solid line for inequalities that include equality (≥ or ≤) and a dashed line for strict inequalities (> or <). Then, shade the appropriate region based on the inequality.

Front

What does the inequality y > -x - 1 represent graphically?

Back

The inequality y > -x - 1 represents the region above the line y = -x - 1.

Front

What does the inequality y ≥ x + 4 represent graphically?

Back

The inequality y ≥ x + 4 represents the region above and including the line y = x + 4.

Front

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

Back

A dashed line indicates that the points on the line are not included in the solution set for strict inequalities (>, <).

Front

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

Back

A solid line indicates that the points on the line are included in the solution set for inclusive inequalities (≥, ≤).

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

Front

What does it mean to shade above a line in a graph?

Back

Shading above a line indicates that the solution includes all points where the y-value is greater than the y-value of the line at any given x-value.

Front

What does it mean to shade below a line in a graph?

Back

Shading below a line indicates that the solution includes all points where the y-value is less than the y-value of the line at any given x-value.

Front

What is the solution set of a system of inequalities?

Back

The solution set of a system of inequalities is the region on the graph where the shaded areas of all inequalities overlap.