graphing systems of Inequalites

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 graph a system of inequalities?

Back

To graph a system of inequalities, first graph each inequality as if it were an equation. Then, use a dashed line for < or > and a solid line for ≤ or ≥. Shade the appropriate region that satisfies the inequality.

Front

What does it mean when a solution set is above a line in a graph?

Back

It means that the inequality is greater than (y > mx + b) or greater than or equal to (y ≥ mx + b).

Front

What does it mean when a solution set is below a line in a graph?

Back

It means that the inequality is less than (y < mx + b) or less than or equal to (y ≤ mx + b).

Front

What is the significance of the intersection of shaded regions in a graph of inequalities?

Back

The intersection of shaded regions represents the solution set that satisfies all inequalities in the system.

Front

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

Back

To determine if a point is a solution, substitute the x and y values of the point into each inequality. If the point satisfies all inequalities, it is part of the solution set.

Front

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

Back

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

Front

What does the inequality y < 2 represent on a graph?

Back

It represents all points below the horizontal line y = 2, not including the line itself.

Front

What does the inequality y ≥ 3x - 1 represent on a graph?

Back

It represents all points on or above the line y = 3x - 1, including the line itself.

Front

How do you find the solution set for a system of inequalities?

Back

Graph each inequality, shade the appropriate regions, and identify the overlapping shaded area, which represents the solution set.