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

How do you determine whether to shade above or below a line in a graph of an inequality?

Back

If the inequality is of the form y ≥ (or >), shade above the line. If it is of the form y ≤ (or <), shade below the line.

Front

What type of line is used to represent y < in a graph?

Back

A dashed line is used to represent y < because the points on the line are not included in the solution.

Front

What type of line is used to represent y ≥ in a graph?

Back

A solid line is used to represent y ≥ because the points on the line are included in the solution.

Front

What does the solution to a system of inequalities represent graphically?

Back

The solution represents the region where the shaded areas of all inequalities overlap.

Front

How do you graph the inequality y > -2x + 3?

Back

1. Graph the line y = -2x + 3 with a dashed line. 2. Shade above the line.

Front

What is the significance of the intersection of two inequalities in a system?

Back

The intersection represents the set of solutions that satisfy both inequalities.

Front

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

Back

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

Front

What is the difference between a solid line and a dashed line in graphing inequalities?

Back

A solid line indicates that points on the line are included in the solution (≥ or ≤), while a dashed line indicates they are not included (> or <).

Front

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

Back

It represents all points below the line y = x + 4.