graphing systems of Inequalites

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?

Back

To graph a linear inequality, first graph the corresponding linear equation as a dashed or solid line, depending on whether the inequality is strict (< or >) or inclusive (≤ or ≥). Then, shade the region that satisfies the inequality.

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 shaded region of the graph.

Front

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

Back

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

Front

How can you determine if a point is a solution to an inequality?

Back

To determine if a point is a solution, substitute the x and y values of the point into the inequality. If the inequality holds true, then the point is a solution.

Front

What is the graphical representation of the inequality y < 2?

Back

The graphical representation is a horizontal line at y = 2, with the area below the line shaded.

Front

What does the inequality y > 2x - 4 represent graphically?

Back

It represents a region above the line y = 2x - 4, which is graphed as a dashed line since the inequality is strict.

Front

How do you solve a system of inequalities by graphing?

Back

To solve by graphing, graph each inequality on the same coordinate plane, shade the appropriate regions, and identify the overlapping shaded area, which represents the solution.

Front

What is the solution set of a system of inequalities?

Back

The solution set is the set of all points that satisfy all inequalities in the system, represented by the overlapping shaded regions on the graph.

Front

What does it mean for two inequalities to be independent?

Back

Two inequalities are independent if the solution to one does not affect the solution to the other, meaning their graphs do not intersect.