System of Inequalities Review

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 represent a linear inequality graphically?

Back

A linear inequality is represented graphically by a line (solid for ≤ or ≥, dashed for < or >) and a shaded region indicating the solution set.

Front

What does the shaded region in a graph of inequalities represent?

Back

The shaded region represents all the possible solutions that satisfy the inequality.

Front

What is the difference between a solid line and a dashed line in graphing inequalities?

Back

A solid line indicates that points on the line are included in the solution (≤ or ≥), while a dashed line indicates that points on the line are not included ( < or >).

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 for a point to be in the overlap of shaded regions?

Back

A point in the overlap of shaded regions satisfies all inequalities in the system, meaning it is a solution to the system.

Front

What is the significance of the intersection of two inequalities?

Back

The intersection of two inequalities represents the set of points that satisfy both inequalities simultaneously.

Front

How can you tell which region to shade when graphing a linear inequality?

Back

To determine which region to shade, test a point not on the line (often (0,0) if it's not on the line) in the inequality. If the inequality holds true, shade the region containing that point.

Front

What is the solution set of the system y ≤ 3x and y ≤ -2x + 4?

Back

The solution set is the region where both inequalities overlap, which can be found by graphing both lines and identifying the shaded area.

Front

What does it mean if a point is not a solution to a system of inequalities?

Back

If a point is not a solution, it means that when substituted into the inequalities, it does not satisfy at least one of them.