1. Model contexts graphically using a system of inequalities
Math 8C Unit 5 – Day 3
Standards:
Use a graph to show the series of solutions to a system of inequalities
Model contexts graphically using a system of inequalities

2. Must Do (12/14):
Solve the system of inequalities by graphing 𝑥+𝑦≥6 𝑦≤𝑥 𝑥+2𝑦≤12
Solution!

3. Writing Systems What are the variables?
You can work at most 20 hours next week. You need to earn at least $96 to cover your weekly expenses. Your dog walking job pays $6 per hour and your job as a car wash attendant pays $8 per hour. You also want to work more hours at the car wash than dog walking. Write a system of linear inequalities to model the situation.
What are the variables?
Write 3 inequalities to represent this situation:
1: To represent the number of hours you can work.
2: To represent the amount of money you need to earn.
3: To represent the division of hours.

4. Writing Systems 𝑥=hours of dog walking 𝑦=hours at car wash
Hours you can work:
Amount of money you need to earn:
Division of hours:
Now graph the system to find the different combinations of hours you can work to meet these constraints.
𝑥=hours of dog walking
𝑦=hours at car wash
𝑥+𝑦≤20
6𝑥+8𝑦≥96
𝑦≥𝑥

5. Solving Larger Systems
Graph the system
𝑥+𝑦≤20
6𝑥+8𝑦≥96
Solution!
𝑦≥𝑥

6. Interpret the Intersections
(0, 20)
6𝑥+8𝑦≤96
𝑥+𝑦≤20
# of hours at the car wash
𝑦≥𝑥
(0, 12)
(10, 10)
(0, 20) = 0 hours of dog walking and 20 hours at the car wash gives you exactly 20 hours of work, more than $96 a week, and is more time at the car wash than dog walking.
(0, 12) = 0 hours of dog walking and 12 hours at the car wash gives you less than 20 hours of work, exactly $96 a week, and is more time at the car wash than dog walking.
(6.9, 6.9)
# of hours dog walking
= 6.9 hours at each job is less than 20 hours a week and earns about $96 a week.
10, 10 = 10 hours at each job is exactly 20 hours a week and earns more than $96/wk

7. Your Task Eileen’s Work Week
(U5D3 – ICP)
Write 3 inequalities to represent Eileen’s situation.
Graph the 3 inequalities and shade in the solution region.
Solve for the intersections using algebra
Explain the meanings of each point of intersection.
Recommend an option for Eileen and explain why you chose it.

8. Must Do (12/15):
Mary babysits for $4 per hour. She also works as a tutor for $8 per hour. She is only allowed to work 13 hours per week, at most. She wants to make at least $65.
Write and graph a system of inequalities to represent this situation.
Make a table with 5 possible solutions.
What do the intersections represent in this context?

9. Must Do (12/16):
Make this based on summative…...