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 linear inequality in two variables?

Back

To graph a linear inequality, first graph the corresponding linear equation as a dashed or solid line. Then, shade the appropriate half-plane based on the inequality symbol.

Front

What does a dashed line indicate in the graph of an inequality?

Back

A dashed line indicates that the points on the line are not included in the solution set (i.e., the inequality is strict, such as < or >).

Front

What does a solid line indicate in the graph of an inequality?

Back

A solid line indicates that the points on the line are included in the solution set (i.e., the inequality is non-strict, such as ≤ or ≥).

Front

What is the solution set of a system of inequalities?

Back

The solution set of a system of inequalities is the region on the graph where the shaded areas of all inequalities overlap.

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 part of the solution set.

Front

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

Back

The boundary line separates the coordinate plane into two half-planes, one of which contains the solutions to the inequality.

Front

What does the term 'half-plane' refer to in the context of inequalities?

Back

A half-plane refers to one of the two regions created by a boundary line in the graph of a linear inequality, where all points satisfy the inequality.

Front

What is the difference between a strict and non-strict inequality?

Back

A strict inequality (< or >) does not include the boundary line, while a non-strict inequality (≤ or ≥) includes the boundary line.

Front

How do you identify a point that is NOT part of the solution set?

Back

A point that does not satisfy at least one of the inequalities in the system is NOT part of the solution set.