Systems 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 region where the graphs of the inequalities overlap.

Front

What does it mean if a system of inequalities has no solution?

Back

It means that there is no set of values for the variables that satisfies all inequalities in the system simultaneously.

Front

What does it mean if a system of inequalities has infinite solutions?

Back

It means that there are countless sets of values for the variables that satisfy all inequalities in the system.

Front

What type of line is used to represent inequalities with symbols \( \leq \) or \( \geq \)?

Back

A solid line is used to represent inequalities with symbols \( \leq \) or \( \geq \) because the points on the line are included in the solution set.

Front

What type of line is used to represent inequalities with symbols \( < \) or \( > \)?

Back

A dotted line is used to represent inequalities with symbols \( < \) or \( > \) because the points on the line are not included in the solution set.

Front

When shading the graph of an inequality, what does shading above the line indicate?

Back

Shading above the line indicates that the solution set includes all points above the line, typically for inequalities of the form \( y > mx + b \) or \( y \geq mx + b \).

Front

When shading the graph of an inequality, what does shading below the line indicate?

Back

Shading below the line indicates that the solution set includes all points below the line, typically for inequalities of the form \( y < mx + b \) or \( y \leq mx + b \).

Front

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

Back

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

Front

What is the graphical representation of the solution set for a system of inequalities?

Back

The solution set is represented by the overlapping shaded regions of the inequalities on a graph.

Front

What does the point (0, 0) represent in the context of a system of inequalities?

Back

The point (0, 0) is a specific coordinate that can be tested to see if it satisfies the inequalities in the system.