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Real Life Systems of Linear Equations Project
Students will understand systems of linear equations and use them to solve problems.
a. Given a problem in context, write an appropriate system of linear equations.
b. Solve systems of equations graphically and algebraically, using technology as appropriate.
c. Interpret solutions in problems context.
 Select one problem from each section to demonstrate your knowledge of how to apply
systems of linear equations to solve problems. You can not choose more than one
problem from each category.
 For each problem, use a new piece of paper divided into three sections.
1. Paste the actual problem on the paper in the section in which you will show how to
work out the problem.
2. Place the name of the category in which the problem belongs at the top of the
section (Graphing, Substitution, Elimination).
3. Write a Systems of Equation to model the given situation.
4. Solve the Systems of Equations.
5. Write a sentence to explain what the solution represents in terms of the problem.
6. Use pictures to illustrate the problem.
7. Your work should be neat. Therefore, you should work out each problem on a
separate piece of paper before transferring your answer to the final copy.
 Create a written response for the following questions in complete sentences:
1. Which method did you find the easiest to complete? Why?
2. Which method did you find the hardest to complete? Why?
Real Life Systems of Linear Equations Project
DUE: ___________________________________
Graphing
Substitution
Equations (2)
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Equations (2)
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Solution (1)
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Solution (1)
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Sentence (1)
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Sentence (1)
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Picture (1)
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Picture (1)
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Elimination
Written Response
Equations (2)
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Question 1 response (1)
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Solution (1)
_____________
Question 2 response (1)
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Sentence (1)
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Complete Sentences (2)
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Picture (1)
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Overall Neatness of Project (2) ________
Grade ____________ out of 21 points
Real Life Systems of Linear Equations Project
GRAPHING
SUBSTITUTION
Joe’s Hamburger Shop sells
540 burgers each day. They sell
hamburgers and turkey burgers.
The hamburgers sold are 39
more than twice the turkey
burgers sold. How many of each
burger are sold a day?
40 adults and 26 kids went to see a
movie on the opening screening and
the revenue for the showing was
$486.70. The next showing 20 adults
and 31 kids went to see the same
movie and the revenue was $332.45.
How much was an adult ticket and
how much was a kid ticket?
At my uncle’s farm, he raises
chickens and pigs. The number of
chickens is four more than three
times the number of pigs. If he has
animals with 148 legs, then how
many of each animal does he have
on the farm?
353 people attend a local play at a
private club. Members get tickets for
$2.75, while non-members have to
pay $6.50. If the total gate for the
play came to $1762, how many
members and non-members came to
the play?
Monica plans to save $5 per week and
already has saved $25. Michael has
$16 and plans to save $8 per week. In
how many weeks will Monica and
Michael have the same amount of
money? How much money will they
have saved?
Quickie-Tricky Internet charges no
monthly charge & $5 per hour to use
their services. D.O.T. com Internet
charges a $15 monthly charge plus $2
per hour to use their services. When
will the companies charge the same
amount? How much will they both
charge?
Hot Dog Health Club charges $25 to
start and $50 per month. Fat-B-Gone
Health Club charges a flat fee of $300.
After how many months will the cost
of the gyms be the same? How much
will the cost be?
The sum of two numbers is 51. The
second number is six less than twice
the first number. Find the two
numbers.
Jim runs a food cart and during a busy
outdoor festival he sold $7343.75
worth of food. He sells hot dogs for
$2.95 and steak sandwiches for $9.95.
If he sold a total of 985 items that
day, how many of each item did he
sell?
You have 15 coins in your pocket.
The coins are either quarters or dimes.
You have a total of $3.15. How many
quarters and dimes do you have?
The sum of twice Leann’s age and
three times Morgan’s age is 30.
Leann is 5 years older than Morgan.
Find their ages.
Alice is counting a cash register at the
end of the night. She has $1015 in $5
bills and $10 bills. If she has 138 bills
all together, how many of each type
does she have?
Horizon Wireless charges $50 plus $10
per GB of data used a month. Monkey
Business charges $25 plus $15 per GB
of data used a month. After how many
GB of data will the cost be the same?
How much will the total bill be?
You are running a concession stand
at the football game. Hotdogs sell
for $2 each and sodas sell for $1
each. At the end of the night, you
made a total of $478. The number
of drinks sold was 10 more than the
number of hotdogs sold. How
many hotdogs and drinks did you
sell?
You are selling tickets at a high
school football game. Student
tickets cost $2 and adult tickets
cost $3. You sell 1957 tickets and
collect $5035. How many of each
type tickets did you sell?
Shantel has two job offers as a car
sales person. At Crazy Cars, she will
receive $600 plus a commission of 2%
of her total sales for the month. At
Sid’s Cars, she will receive $1000 plus
a commission of 1.5% of her total
sales. What is the total sales amount
Shantel must meet each month to make
the same income from either
dealership? What will her income be
from that amount of sales?
Hot air balloon #1 is 10 meters about
the ground, rising 15 meters per
minute. Hot air balloon #2 is 150
meters above the air descending 20
meters per minute. In how many
minutes will the balloons be the same
height? How high will the balloons be
at that time?
There are 34 students in
Mrs. Noell’s class. There are
eight more boys than girls. How
many boys and girls are in her
class?
ELIMINATION