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 ordered pairs that satisfy all inequalities in the system.

Front

How do you determine if an ordered pair is a solution to a system of inequalities?

Back

To determine if an ordered pair is a solution, substitute the values of the ordered pair into each inequality. If the pair satisfies all inequalities, it is a solution.

Front

What does it mean for a point to be a solution of a system of inequalities?

Back

A point is a solution of a system of inequalities if it lies in the region where all inequalities overlap on a graph.

Front

What is the graphical representation of a system of inequalities?

Back

The graphical representation consists of shaded regions on a coordinate plane, where each region corresponds to the solutions of each inequality.

Front

What is the significance of the boundary lines in a system of inequalities?

Back

Boundary lines represent the limits of the inequalities. If the inequality is strict (e.g., < or >), the line is dashed; if it is inclusive (e.g., ≤ or ≥), the line is solid.

Front

What does it mean if a point lies on a dashed line in a graph of inequalities?

Back

If a point lies on a dashed line, it means that the point is not included in the solution set for that inequality.

Front

What does it mean if a point lies on a solid line in a graph of inequalities?

Back

If a point lies on a solid line, it means that the point is included in the solution set for that inequality.

Front

How can you find the solution set of 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 an ordered pair?

Back

An ordered pair is a pair of numbers used to represent a point in a two-dimensional space, written in the form (x, y).

Front

What is the difference between a solution and a non-solution in the context of inequalities?

Back

A solution satisfies all inequalities in the system, while a non-solution does not satisfy at least one inequality.