Lesson 3.2.2: Solving Systems of Inequalities

​Lesson 3.2.2: Solving Systems of Inequalities

By Sarah Herbert

Poll

In your opinion, which graph does not belong with the other three?

• A

• B

• C

• D

Reminders

Inequalities that use "or equal to" are graphed with a solid boundary line, and the solutions to the inequality can lie on the boundary line. Think about what this means for systems of inequalities.

Categorize

Options (5)

(0, 5)

(-6, 6)

(3, -5)

(3, 3)

(-2, -2)

Determine whether the ordered pair is a solution to the system of inequalities.

Solution

Not a Solution

Consider this Situation

To participate in a competition, each team must follow the rules below. Let x represent the number of children on the team, and let y represent the number of adults. Develop a system of inequalities to model the problem.

1) A team with no adults is allowed.
2) There must be 2 children for every 1 adult.
3) A team can have no more than 16 members in total.

Dropdown

Complete the inequality that represents: "A team with no adults is allowed."

y​

Select answer

0

Dropdown

Complete the inequality that represents: "There must be two children for every one adult." x​

Select answer

2y

Drag and Drop

Complete the inequality that represents: "A team can have no more than 16 members total."

Placeholder

$$\le$$ 16

Drag these tiles and drop them in the correct blank above

x+y

2x + 2y

x-y

xy

Draw

Graph the system of inequalities:

$$y\ge0$$

$$x\ge2y$$

$$x+y\le16$$

Open Ended

How would you describe a team with 14 children and 5 adults?

Draw

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.

Draw

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.

Draw

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

Draw

Graph the system of inequalities on the coordinate plane:

$$x<4$$

$$x+y<12$$

Labelling

Label the solution region to the system of inequalities.

Drag labels to their correct position on the image

solution

not the solution

not the solution

not the solution

Multiple Select

View the image to answer the question.

• The combination of 7.5 cubic feet of topsoil and 12 cubic feet of compost is within the budget.

• 5 cubic feet of topsoil and 20 cubic feet of compost is within the budget.

• $$1.89t+4.59c\le70$$

• $$1.89t+4.59c\ge70$$