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 system of inequalities?

Back

1. Graph each inequality on the same coordinate plane. 2. Use a dashed line for < or > and a solid line for ≤ or ≥. 3. Shade the region that satisfies each inequality. 4. The solution set is where the shaded regions overlap.

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 inequalities in the system, meaning it lies in the overlapping shaded region of the graph.

Front

What is the difference between '>' and '≥' in inequalities?

Back

'>' means that the value is strictly greater than, while '≥' means that the value is greater than or equal to.

Front

What does the shaded area above a line in a graph of an inequality represent?

Back

The shaded area above a line represents all the points (x, y) that satisfy the inequality y > mx + b, where m is the slope and b is the y-intercept.

Front

What does the shaded area below a line in a graph of an inequality represent?

Back

The shaded area below a line represents all the points (x, y) that satisfy the inequality y < mx + b, where m is the slope and b is the y-intercept.

Front

How can you determine if a point is part of the solution set for 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 is the significance of the intersection of shaded regions in a graph of inequalities?

Back

The intersection of shaded regions represents the solution set of the system of inequalities, where all conditions are satisfied.

Front

What does it mean if a line is dashed in a graph of an inequality?

Back

A dashed line indicates that the points on the line are not included in the solution set, meaning the inequality is strict (either < or >).

Front

What does it mean if a line is solid in a graph of an inequality?

Back

A solid line indicates that the points on the line are included in the solution set, meaning the inequality is non-strict (either ≤ or ≥).