5.6 Systems of Inequalities Practice

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

Front

How do you determine if a point is a solution to a system of inequalities?

Back

To determine if a point is a solution, substitute the point's coordinates into each inequality. If the point satisfies all inequalities, it is a solution.

Front

What does it mean if a point is a solution to a system of inequalities?

Back

It means that the point lies in the region where all inequalities overlap on a graph.

Front

What type of line is used when graphing the inequalities 'y < mx + b' or 'y > mx + b'?

Back

A dotted line is used to indicate that the points on the line are not included in the solution.

Front

What type of line is used when graphing the inequalities 'y ≤ mx + b' or 'y ≥ mx + b'?

Back

A solid line is used to indicate that the points on the line are included in the solution.

Front

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

Back

The symbol '≤' 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

The symbol '>' means 'greater than', indicating that the value must be strictly greater than a certain number.

Front

How do you graph the inequality 'y ≤ 2x - 1'?

Back

Graph the line y = 2x - 1 with a solid line, then shade below the line to represent all points where y is less than or equal to 2x - 1.

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

What does it mean if a system of inequalities has no solution?

Back

It means that there is no point that satisfies all inequalities in the system, often represented by parallel lines that never intersect.