Name: _____________________
Class: _________________
AU4: Lesson 7 - Systems of Equations Task
1.
Consider the graph below showing two lines, L1 and L2.
a. What is the solution to the above system?
b. Find the two corresponding linear equations.
c. Find a point other than the ones given in the graph that lies on L1 but not on L2.
d. Find a point other than the ones given in the graph that lies on L2 but not on L1.
1
2.
You work for a video streaming company that has two monthly plans to choose from:
Plan 1: A flat rate of $7 per month plus $2.50 per video viewed
Plan 2: $4 per video viewed
a. What type of functions model this situation? Explain how you know.
b. Define variables that make sense in the context, and then write an equation with cost as
a function of videos viewed, representing each monthly plan.
c. How much would 3 videos in a month cost for each plan? 5 videos?
d. Compare the two plans and explain what advice you would give to a customer trying
to decide which plan is best for them, based on their viewing habits.
2
3.
A theater charges $9 for each adult ticket and $6 for each child ticket. The theater sold
144 tickets for the first showing of the new release. The total money collected from ticket
sales for that show was $1164. Write a system of equations that could be used to find the
number of child tickets and the number of adult tickets sold and solve the system
algebraically.
3
4.
Consider the equation 5 x  2 y  3 . If possible, find a second linear equation to create a
system of equations that has the following solution(s). Show work or explain.
a. Exactly 1 solution.
b. Exactly 2 solutions.
c. No solutions.
d. Infinitely many solutions.
4
5.
The local theater in Jamie’s home town has a maximum capacity of 160 people. Jamie
shared with Venus the following graph and said that the shaded region represented all the
possible combinations of adult and child tickets that could be sold for one show.
a.
Venus objected and said there was more than one reason that Jamie’s thinking was
flawed. What reasons could Venus be thinking of?
b.
Use equations, graphs and/or words to describe for Jamie the set of all possible
combinations of adult and child tickets that could be sold for one show.
5
6.
A jeweler plans to produce a ring made of silver and gold. The price of gold is
approximately $10/gram. The price of silver is approximately $0.15/g. She considers the
following in deciding how much gold and silver to use in the ring:



Let:
The total mass must be more than 10 grams but less than 20 grams.
The ring must contain at least 3g of gold.
The total cost of the gold and silver must be less than $60.
x = mass of silver in grams
y = mass of gold in grams
Part A: Write and graph the four inequalities that describe this situation
y
x
Part B:
For one solution (x, y), find the total mass of the ring and the cost of the gold in the ring.
6