Systems of Linear Inequalities

Front

What is a system of linear inequalities?

Back

A system of linear 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

What does the symbol '≤' represent in an inequality?

Back

'≤' means 'less than or equal to', indicating that the value can be less than or equal to a certain number.

Front

What does the symbol '≥' represent in an inequality?

Back

'≥' means 'greater than or equal to', indicating that the value can be greater than or equal to a certain number.

Front

When do you use a solid line when graphing inequalities?

Back

A solid line is used when the inequality includes '≤' or '≥', indicating that points on the line are included in the solution set.

Front

When do you use a dashed line when graphing inequalities?

Back

A dashed line is used when the inequality includes '<' or '>', indicating that points on the line are not included in the solution set.

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 part of the solution set.

Front

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

Back

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

Front

What does it mean if a point lies outside the shaded region of a graph of inequalities?

Back

If a point lies outside the shaded region, it does not satisfy at least one of the inequalities in the system.

Front

What is the significance of the intersection of two inequalities?

Back

The intersection represents the set of solutions that satisfy both inequalities simultaneously.

Front

How can you identify the solution set from a graph of linear inequalities?

Back

The solution set is identified by the shaded area where the solutions to the inequalities overlap.