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 for inequalities with symbols < or >?

Back

A dotted line is used for inequalities with symbols < or > to indicate that points on the line are not included in the solution.

Front

What type of line is used for inequalities with symbols ≤ or ≥?

Back

A solid line is used for inequalities with symbols ≤ or ≥ to indicate that points on the line are included in the solution.

Front

Back

Front

Back

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

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

Back

Front

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

Back

The boundary line separates the solution region from the non-solution region. Points on the line may or may not be included based on the inequality symbol.