This document discusses systems of inequalities and how to solve them by graphing. It explains that a system of inequalities can have many solutions, where a solution satisfies each individual inequality. The key steps are to graph each inequality, find the overlap of the solutions, and use a test point to check the solution set. An example word problem about fundraising ticket sales is provided to demonstrate solving a system of inequalities.

1. 3.3 Systems of Inequalities

2. Systems of Inequalities An inequality and a system of inequalities have many solutions. A solution of a system of inequalities is a solution for each inequality in the system.

3. Solving a System of inequalities Graphing is usually the most appropriate method The solution is the set of all points that are solutions of each inequality in the system Graph the first inequality Graph the second inequality The solution is the overlap of the two half-plane solutions from steps 1 & 2 To check, use a test point

4. Solve the system by graphing

5. Solve the system by graphing

6. Solve the system by graphing

7. Word Problems: Fundraising You city’s cultural center is sponsoring a concert to raise at least $30,000 for the city’s Youth Services. Tickets are $20 for balcony seats and $30 for orchestra seats. If the center has 500 orchestra seats, how many of each type of seat must they sell?