Graphing Systems of Inequalities and Equations

Front

What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities that share the same variables. The solution is the set of all points that satisfy all inequalities in the system.

Front

What does it mean to graph an inequality?

Back

Graphing an inequality involves drawing a line (or curve) on a coordinate plane that represents all the solutions to the inequality. The area above or below the line indicates the solutions.

Front

When do you use a solid line when graphing inequalities?

Back

A solid line is used when the inequality includes '≤' or '≥', indicating that points on the line are included in the solution set.

Front

What does a dashed line represent in graphing inequalities?

Back

A dashed line represents that the points on the line are not included in the solution set, used for inequalities with '<' 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 coordinates of the point into each inequality. If the point satisfies all inequalities, it is part of the solution set.

Front

What is the solution set of a system of inequalities?

Back

The solution set is the region on the graph where the shaded areas of all inequalities overlap, representing all possible solutions.

Front

How do you graph the inequality y < 2x + 3?

Back

Graph the line y = 2x + 3 with a dashed line, then shade below the line to represent all points where y is less than 2x + 3.

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, which is the solution to the system.

Front

What does it mean if a point lies on the boundary line of an inequality?

Back

If a point lies on the boundary line, it may or may not be included in the solution set, depending on whether the inequality is strict or non-strict.

Front

How can you check if a point is part of the solution set for a system of inequalities?

Back

Substitute the point's coordinates into each inequality. If it satisfies all inequalities, it is part of the solution set.