Graphing systems of Inequalities

Front

What is a system of inequalities?

Back

A set of two or more inequalities with the same variables that are graphed on the same coordinate plane.

Front

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

Back

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

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 (for inequalities using < or >).

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 (for inequalities using ≤ or ≥).

Front

How do you graph the inequality y > 2x - 4?

Back

Graph the line y = 2x - 4 as a dashed line, then shade above the line.

Front

What is the significance of shading in graphing inequalities?

Back

Shading indicates the region of the graph that represents all possible solutions to the inequality.

Front

What does the inequality y ≤ 2 mean in terms of graphing?

Back

It means that the line y = 2 is solid, and the area below the line is shaded.

Front

How can you tell which direction to shade when graphing a system of inequalities?

Back

Use test points or the inequality sign: shade above the line for > or ≥, and below for < or ≤.

Front

What is the solution set of a system of inequalities?

Back

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

Front

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

Back

It represents a vertical dashed line at x = -2, with shading to the right.