Systems of Inequalities Review

Front

What is a system of inequalities?

Back

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 linear inequality?

Back

1. Graph the corresponding linear equation as a dashed (for < or >) or solid line (for ≤ or ≥). 2. Shade the region that satisfies the inequality.

Front

What does the inequality y ≤ 3x represent?

Back

It represents all points on or below the line y = 3x.

Front

What is the meaning of the solution set in a system of inequalities?

Back

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

Front

How do you determine if a point is in the solution set of a system of inequalities?

Back

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

Front

What does the inequality 3b + 6t > 66 represent in JoAnn's job scenario?

Back

It represents the condition that JoAnn's total earnings from babysitting (b) and tutoring (t) must be greater than $66.

Front

What is the maximum number of hours JoAnn can work?

Back

JoAnn can work a maximum of 15 hours per week.

Front

What does a dashed line indicate when graphing an inequality?

Back

A dashed line indicates that points on the line are not included in the solution set (for < or > inequalities).

Front

What does a solid line indicate when graphing an inequality?

Back

A solid line indicates that points on the line are included in the solution set (for ≤ or ≥ inequalities).

Front

Which point is NOT part of the solution set for the given inequalities: (0, 0), (0, 1), (-100, -3), (5, 10)?

Back

(5, 10) is NOT part of the solution set.