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 ordered pairs that satisfy all inequalities in the system.

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a solid line (for ≤ or ≥) or a dashed line (for < or >). Then, shade the region that satisfies the inequality.

Front

What does a dotted line represent in the graph of an inequality?

Back

A dotted line represents that the points on the line are not included in the solution set, which occurs when the inequality symbol is < or >.

Front

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

Back

A solid line represents that the points on the line are included in the solution set, which occurs when the inequality symbol is ≤ or ≥.

Front

What is the solution to a system of inequalities?

Back

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

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 the point satisfies all inequalities, it is a solution.

Front

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

Back

The boundary line divides the coordinate plane into two regions: one that satisfies the inequality and one that does not.

Front

What is the difference between strict and non-strict inequalities?

Back

Strict inequalities (<, >) do not include the boundary line, while non-strict inequalities (≤, ≥) do include the boundary line.

Front

How do you solve a system of inequalities by graphing?

Back

To solve a system of inequalities by graphing, graph each inequality on the same coordinate plane and identify the overlapping shaded region.

Front

What is the role of the y-intercept in graphing linear inequalities?

Back

The y-intercept is the point where the line crosses the y-axis and is used to plot the line for the corresponding linear equation.