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 linear inequalities that share the same variables. The solution is the set of all points that satisfy all inequalities in the system.

Front

Are the points on the boundary line part of the solution set?

Back

Yes, they are part of the solution set.

Front

How can I tell if an inequality will have a solid line?

Back

The symbol has 'or equal to.'

Front

What does a dashed line represent in a graph of an inequality?

Back

A dashed line indicates that the points on the line are not included in the solution set.

Front

What does a solid line represent in a graph of an inequality?

Back

A solid line indicates that the points on the line are included in the solution set.

Front

What is the solution set of a system of inequalities?

Back

The solution set is the region on the graph where the shaded areas of all inequalities overlap.

Front

How do you graph a linear inequality?

Back

1. Graph the boundary line (solid or dashed). 2. Choose a test point to determine which side of the line to shade.

Front

What is the significance of the intersection point of two lines in a system of inequalities?

Back

The intersection point represents a solution that satisfies both inequalities.

Front

If a system of inequalities has no intersection, what does that mean?

Back

It means there is no solution to the system; the inequalities are contradictory.

Front

What is the difference between 'greater than' and 'greater than or equal to' in inequalities?

Back

'Greater than' uses a dashed line and does not include the boundary, while 'greater than or equal to' uses a solid line and includes the boundary.