System of Inequalities

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

To graph a system of inequalities, first graph each inequality as if it were an equation. Use a dashed line for < or > and a solid line for ≤ or ≥. Then, shade the appropriate region for each inequality, and the solution is where the shaded regions overlap.

Front

What does it mean for a point to be 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 a solid line and a dashed line in graphing inequalities?

Back

A solid line indicates that the points on the line are included in the solution (≤ or ≥), while a dashed line indicates that the points on the line are not included ( < or >).

Front

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

Back

To determine if a point is a solution, substitute the x and y values of the point into each inequality. If the point satisfies all inequalities, it is a solution.

Front

What is the maximum number of hours you can work if you have a constraint of 20 hours?

Back

You can work at most 20 hours, which means the total hours worked in all jobs combined cannot exceed 20.

Front

If a tutoring job pays $7.50 per hour, how much will you earn for 5 hours?

Back

You will earn $37.50 for 5 hours of tutoring (5 hours x $7.50/hour).

Front

What is the inequality that represents earning at least $92?

Back

The inequality is 6s + 7.50t ≥ 92, where s is the hours worked as a pet sitter and t is the hours worked as a tutor.

Front

What does the inequality s + t ≤ 20 represent?

Back

This inequality represents the total hours worked in both jobs (s for pet sitting and t for tutoring) cannot exceed 20 hours.

Front

What is a feasible region in the context of a system of inequalities?

Back

The feasible region is the area on the graph where all the shaded regions of the inequalities overlap, representing all possible solutions.