Systems of Inequalities

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 graph a system of inequalities?

Back

To graph a system of inequalities, first graph each inequality as if it were an equation. Then, shade the region that satisfies the inequality. The solution set is where the shaded regions overlap.

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 inequalities in the system, meaning it lies in the overlapping shaded region of the graph.

Front

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

Back

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

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

Front

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

Back

The boundary line represents the points where the inequality changes from true to false. 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 above a boundary line in a graph of an inequality?

Back

If a point lies above a boundary line in a graph of an inequality, it means that the point satisfies the inequality represented by that line.

Front

What does it mean if a point lies below a boundary line in a graph of an inequality?

Back

If a point lies below a boundary line in a graph of an inequality, it means that the point does not satisfy the inequality represented by that line.

Front

What is a feasible region in the context of systems of inequalities?

Back

The feasible region is the area on the graph where all the shaded regions of the inequalities overlap. It represents all possible solutions to the system.

Front

How do you identify a point that is not a solution to a system of inequalities?

Back

A point that is not a solution will fail to satisfy at least one of the inequalities when its coordinates are substituted into the inequalities.