Solving Systems of Inequalities

Front

What is a system of inequalities?

Back

A set of two or more inequalities with the same variables.

Front

How do you represent a system of inequalities graphically?

Back

By shading the regions that satisfy all inequalities in the system.

Front

What does a dashed line indicate in graphing inequalities?

Back

It indicates that the points on the line are not included in the solution (for < or > inequalities).

Front

What does a solid line indicate in graphing inequalities?

Back

It indicates that the points on the line are included in the solution (for ≤ or ≥ inequalities).

Front

What is the solution to a system of inequalities?

Back

The set of all points that satisfy all inequalities in the system.

Front

If a system of inequalities has no overlapping shaded regions, what does that mean?

Back

It means there is no solution to the system.

Front

What is the significance of the boundary line in a system of inequalities?

Back

It separates the solution region from the non-solution region.

Front

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

Back

Substitute the point into each inequality; if it satisfies all, it is a solution.

Front

What is the difference between a strict inequality and a non-strict inequality?

Back

A strict inequality (< or >) does not include the boundary, while a non-strict inequality (≤ or ≥) does.

Front

Can a system of inequalities have infinitely many solutions?

Back

Yes, if the shaded regions overlap, there can be infinitely many solutions.