Practice Graphing System of Inequalities

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 if a point is a solution to a system of inequalities?

Back

A point is a solution to a system of inequalities if it satisfies all the inequalities in the system, meaning it makes all inequalities true.

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 a solution.

Front

What does the inequality y ≥ represent graphically?

Back

The inequality y ≥ represents the region above the line y = x, including the line itself.

Front

What does the inequality y < represent graphically?

Back

The inequality y < represents the region below the line y = x, excluding the line itself.

Front

What is the significance of shading in graphing inequalities?

Back

Shading indicates the region of the graph that contains all the solutions to the inequality. The direction of shading depends on the inequality sign.

Front

What does it mean for a system of inequalities to have no solution?

Back

A system of inequalities has no solution if there is no point that satisfies all inequalities simultaneously, often resulting in parallel lines that never intersect.

Front

What is the graphical representation of the solution set for a system of inequalities?

Back

The solution set is represented by the overlapping shaded regions of the inequalities on a graph.

Front

How do you graph the inequality 2x + 3y < 6?

Back

First, graph the line 2x + 3y = 6 as a dashed line (since it's <). Then shade below the line to represent all points (x, y) 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 <).