Graphing systems of Inequalities

Front

What is a system of inequalities?

Back

A set of two or more inequalities with the same variables, representing a region on a graph where all inequalities are satisfied.

Front

What does it mean for a point to be a solution to a system of inequalities?

Back

A point is a solution if it satisfies all inequalities in the system, meaning it lies in the overlapping shaded region on the graph.

Front

How do you determine if a point is a solution to a system of inequalities?

Back

Substitute the coordinates of the point into each inequality. If the point satisfies all inequalities, it is a solution.

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 they are not included (> or <).

Front

What does the inequality y > mx + b represent?

Back

It represents the region above the line y = mx + b, where all points (x, y) satisfy the inequality.

Front

What does the inequality y ≤ mx + b represent?

Back

It represents the region below the line y = mx + b, including the line itself, where all points (x, y) satisfy the inequality.

Front

What is the significance of parallel lines in a system of inequalities?

Back

Parallel lines indicate that the inequalities do not intersect, which may result in no solution or a solution that is not bounded.

Front

How can you graph a system of inequalities?

Back

1. Graph each inequality as if it were an equation. 2. Use solid or dashed lines as appropriate. 3. Shade the correct region for each inequality. 4. Identify the overlapping shaded region.

Front

What does it mean if two inequalities in a system are contradictory?

Back

It means that there is no point that can satisfy both inequalities simultaneously, resulting in no solution.

Front

What is the role of the boundary line in graphing inequalities?

Back

The boundary line separates the graph into two regions: one that satisfies the inequality and one that does not.