Systems of Inequalities

Front

What is a system of inequalities?

Back

A set of two or more inequalities with the same variables that are solved together.

Front

What does the symbol '≥' mean?

Back

It means 'greater than or equal to'.

Front

What does the symbol '≤' mean?

Back

It means 'less than or equal to'.

Front

How do you graph the inequality y > -x - 1?

Back

Graph the line y = -x - 1 as a dashed line and shade above it.

Front

How do you graph the inequality y ≤ x + 3?

Back

Graph the line y = x + 3 as a solid line and shade below it.

Front

What is the solution set of a system of inequalities?

Back

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

Front

How can 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 does it mean if a point lies on a dashed line in a graph of inequalities?

Back

The point is not included in the solution set for that inequality.

Front

What does it mean if a point lies on a solid line in a graph of inequalities?

Back

The point is included in the solution set for that inequality.

Front

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

Back

It represents the solution set of the system of inequalities.