System of Inequalities Review

Front

What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities that share the same variables. The solution is the set of all points that satisfy all inequalities in the system.

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding equation as a line. Use a solid line for '≤' or '≥' and a dashed line for '<' or '>'. Then, shade the region that satisfies the inequality.

Front

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

Back

A point is a solution to a system of inequalities if it satisfies all inequalities in the system, meaning it lies in the shaded region of the graph.

Front

What is the significance of the overlap in the shaded regions of a system of inequalities?

Back

The overlap in the shaded regions represents the solution set of the system of inequalities, where all conditions are satisfied.

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 the inequality symbol '>' indicate in a graph?

Back

The symbol '>' indicates that the region above the line is included in the solution set, meaning points in that region satisfy the inequality.

Front

What does the inequality symbol '<' indicate in a graph?

Back

The symbol '<' indicates that the region below the line is included in the solution set, meaning points in that region satisfy the inequality.

Front

What is the difference between '≤' and '<' in inequalities?

Back

'≤' means the line is included in the solution set (solid line), while '<' means the line is not included (dashed line).

Front

How do you find the solution set for a system of inequalities?

Back

To find the solution set, graph each inequality, shade the appropriate regions, and identify the overlapping shaded area.

Front

What is the role of the boundary line in a linear inequality?

Back

The boundary line separates the graph into two regions: one that satisfies the inequality and one that does not.