Systems of Linear Inequalities

Front

What is a system of linear inequalities?

Back

A set of two or more linear inequalities involving the same variables.

Front

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

Back

It indicates that the value on the left is less than or equal to the value on the right.

Front

What does the symbol '>' indicate in an inequality?

Back

It indicates that the value on the left is greater than the value on the right.

Front

How do you represent a solution to a system of linear inequalities graphically?

Back

By shading the region of the graph that satisfies all inequalities in the system.

Front

What type of line is used when graphing 'y < mx + b'?

Back

A dashed line, indicating that points on the line are not included in the solution.

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

By substituting the point's coordinates into each inequality and checking if all inequalities are satisfied.

Front

What does it mean if a point lies on the boundary line of an inequality?

Back

It means that the point satisfies the equation of the line, but whether it is included in the solution depends on the inequality symbol.

Front

What is the difference between 'y ≤ mx + b' and 'y < mx + b'?

Back

'y ≤ mx + b' includes the line (solid line), while 'y < mx + b' does not (dashed line).

Front

What is the significance of the shading in a graph of inequalities?

Back

Shading indicates the region where all solutions to the inequalities exist.