Lesson 3.2.2: Solving Systems of Inequalities

Graph the system of inequalities:

$$y\ge0$$

$$x\ge2y$$

$$x+y\le16$$

For another competition, (1) a team must have at least one adult, (2) a team must have three children for every one adult, and (3) the number of people cannot exceed 20. Pick one of these three rules and write the inequality to model it.

A family has at most $25 to spend at the Fun Zone. It costs $10 an hour to use the trampolines and $5 an hour to use the pool. The family can stay less than 4 hours. Write the system of inequalities to model the problem. On the next page, use the graph to graph the system.

Use the Desmos Graphing Calculator to graph the system, and then provide at least three ordered pairs that are solutions. What do they represent?

Graph the system of inequalities on the coordinate plane:

$$x<4$$

$$x+y<12$$