Graphing systems of Inequalities

Front

What is a system of inequalities?

Back

A set of two or more inequalities with the same variables. The solution is the region where the graphs of the inequalities overlap.

Front

What does it mean if an inequality is 'strict'?

Back

A strict inequality uses '>' or '<', meaning the boundary line is not included in the solution set.

Front

What does it mean if an inequality is 'non-strict'?

Back

A non-strict inequality uses '≥' or '≤', meaning the boundary line is included in the solution set.

Front

How do you graph a linear inequality?

Back

1. Graph the boundary line as if it were an equation. 2. Use a solid line for '≥' or '≤' and a dashed line for '>' or '<'. 3. Shade the region that satisfies the inequality.

Front

What is the solution set of a system of inequalities?

Back

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

Front

How can 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 part of the solution set.

Front

What does the graph of y > mx + b look like?

Back

It is a region above the line y = mx + b, with a dashed line indicating that points on the line are not included.

Front

What does the graph of y ≤ mx + b look like?

Back

It is a region below the line y = mx + b, with a solid line indicating that points on the line are included.

Front

What is the significance of the boundary line in a system of inequalities?

Back

The boundary line separates the solution set from the non-solution set and indicates whether points on the line are included based on the type of inequality.

Front

What is the difference between 'y < mx + b' and 'y ≤ mx + b'?

Back

'y < mx + b' means the line is dashed and points on the line are not included; 'y ≤ mx + b' means the line is solid and points on the line are included.