ALG 2 Graphing Inequalities and Systems

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

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

Back

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

Front

What type of line is used to represent an inequality with a < or > sign?

Back

A dashed line is used to represent an inequality with a < or > sign, indicating that points on the line are not included in the solution set.

Front

What type of line is used to represent an inequality with a ≤ or ≥ sign?

Back

A solid line is used to represent an inequality with a ≤ or ≥ sign, indicating that points on the line are included in the solution set.

Front

How do you graph a system of inequalities?

Back

To graph a system of inequalities, graph each inequality on the same coordinate plane, shading the region that satisfies each inequality. The solution set is where the shaded regions overlap.

Front

What is the feasible region in a system of inequalities?

Back

The feasible region is the area on the graph where all the shaded regions of the inequalities overlap, representing all possible solutions.

Front

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

Back

If there is no overlapping region, it means that there is no solution to the system of inequalities.

Front

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

Back

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

Front

What is the maximum number of items that can be purchased if the total cost must not exceed a certain amount?

Back

To find the maximum number of items, set up a system of inequalities based on the cost and quantity constraints, then graph to find the feasible region.

Front

What does it mean for a solution to be 'bounded' in a system of inequalities?

Back

A solution is 'bounded' if the feasible region is enclosed by the lines of the inequalities, meaning there is a limit to the possible solutions.