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Resources

Solve a system of equations using any method

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-x + 3y = -11

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x = -10

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x = -9

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6x - 5y = -4

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10x + 8y = -10

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y = -10

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y = -4

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-3x - 9y = 18

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5x - 8y = 10

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y = 5

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y = -2

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4x - 5y = 6

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y = 8

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9x + 3y = 15

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y = 8

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–10x + 10y = 10

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y = -6

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-10x + 5y = 20

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y = 7

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9x - 5y = 10

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-2x - 2y = 2

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y = -4

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-3x - y = 3

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x = -4

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y = -9

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-7x - 8y = 2

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-4x - y = 7

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y = -3

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x - 3y = 4

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x = -8

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x = -1

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-8x - 6y = 14

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y = 8

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6x - 9y = -12

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-9x - 8y = 11

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y = 2

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2x - y = -6

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x = 2

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x = 3

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–6x + 5y = 17

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y = 10

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3x + 4y = 13

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-3x - y = 12

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y = -9

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y = -3

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9x + 8y = -6

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y = 5

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8x - 5y = 15

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7x + 10y = -20

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x = 10

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x = 5

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9x + 10y = -5

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y = 7

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9x - 10y = 11

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y = 5

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–3x + 4y = 11

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10x - 7y = 8

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x = -2

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7x + 8y = -15

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x = 7

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y = 5

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8x + 8y = 8

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4x + 2y = 4

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y = 10

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x = 2

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9x - y = 17

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10x - 7y = 12

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x = -3

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x = -9

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-4x - 4y = 12

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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

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Kylie and Fernando, the boy she was babysitting, were playing basketball together. Her score was

20

points, and his score was

19

points. Kylie wanted to make the game more fair, so she called a time-out and modified the rules a bit. Kylie explained that, for the rest of the game, she would get

3

points per basket, and Fernando would get

4

points per basket. Then they played a bit longer. After the time-out, they both made the same number of baskets and ended up with a tied score. How many baskets did each person make after the time out? How many points did each person have at the end?

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Kylie and Fernando each made

\_

baskets after the time-out, for a score of

\_

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

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Gavin works in the shipping department of a toy manufacturer. Toy cars weigh

1

kilogram apiece and are shipped in a container that weighs

7

kilograms when empty. Toy trucks, which weigh

2

kilograms apiece, are shipped in a container weighing

4

kilograms. When packed with toys and ready for shipment, both kinds of containers have the same number of toys and the same weight. What is the number of toys? What is the weight of each container?

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\_\_

toys in each container, for a total weight of

\_\_

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

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Sadie, a caterer, is investing some money in equipment and employees to help grow her business. Recently she spent

\$51

on equipment and hired a server who makes

\$14

per hour. Sadie is hoping to make up these expense at the next job that is scheduled, which pays a base of

\$48

\$15

per hour that the server works. In theory, this event could pay enough to cancel out Sadie's expenditures. How much would the job pay? How long would the job have to be?

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The expenditures and pay would both be

\$\_\_\_\_\_

if the job lasted for

\_\_\_\_\_

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

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Substitute teachers with Norwood School District get paid by the day, although subs with teaching credentials earn a different amount than subs without credentials. Yesterday,

3

non-credentialed subs and

10

credentialed subs taught in the district. That cost the district

\$1,107

5

non-credentialed subs and

10

credentialed subs taught, receiving

\$1,205

from the district. How much do subs get paid?

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Subs without credentials get paid

\$

_____ per day, and subs with credentials get paid

\$

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

\newline

Mario's Pizza just received two big orders from customers throwing parties. The first customer, Melissa, bought

4

regular pizzas and

3

deluxe pizzas and paid

\$111

. The second customer, Pablo, ordered

3

regular pizzas and

10

deluxe pizzas, paying a total of

\$246

. What is the price of each pizza?

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Each regular pizza costs

\$

_____, and each deluxe pizza costs

\$

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

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Gabrielle has a home-based business making corsages and boutonnieres for school dances. Last year, she sold

18

37

boutonnieres, which brought in a total of

\$1,121

. This year, she sold

28

19

boutonnieres, for a total of

\$857

. How much does each item sell for?

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A corsage sells for

\$

_____, and a boutonniere sells for

\$

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

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This morning, Cameron processed two catering orders at the sandwich shop where he works. The first order was for

5

trays of club sandwiches and

7

trays of vegetarian sandwiches, at a cost of

\$63

. The second order, which cost

\$59

5

trays of club sandwiches and

6

trays of vegetarian sandwiches. How much do the trays cost?

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A tray of club sandwiches costs

\$

_____, and a tray of vegetarian sandwiches costs

\$

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

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Castroville Photography Studio is taking graduation portraits for students at local schools. Eighth graders from Castroville Elementary School ordered

75

basic portrait packages and

89

deluxe portrait packages, for a total of

\$13,204

. The seniors at Weston High ordered

52

basic portrait packages and

98

deluxe portrait packages, for a total of

\$12,276

. How much does each type of package cost?

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A basic package costs

\$

_____, and a deluxe package costs

\$

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

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Kira, an office manager, needs to find a courier to deliver a package. The first courier she is considering charges a fee of

\$16

\$6

per kilogram. The second charges

\$12

\$7

per kilogram. Kira determines that, given her package's weight, the two courier services are equivalent in terms of cost. What is the weight? How much will it cost?

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At a package weight of

\_\_

kilograms, the two couriers both cost

\$\_\_\_\_\_

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

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Percy and his mom are planting vegetables in their garden. Percy has finished planting

8

rows of carrots so far and is planting new rows at a rate of

4

rows per hour. His mom has finished

6

rows of tomatoes and will continue planting at

5

rows per hour. Once the pair get to the point where they have finished the same number of rows, they will take a break and decide what to plant next. How many rows will they each have completed? How long will that take?

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Percy and his mom will each be done planting

\_\_\_

\_\_\_

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

\newline

Chloe is a salon owner. Yesterday, she did

4

haircuts and colored the hair of

3

clients, charging a total of

\$388

. Today, she did

4

haircuts and colored the hair of

4

clients, charging a total of

\$460

. How much does Chloe charge for her services?

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\$

_____ for a haircut and

\$

_____ for a coloring.

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

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Evan wants to take group fitness classes at a nearby gym, but needs to start by selecting a membership plan. With the first membership plan, Evan can pay

\$48

per month, plus

\$2

for each group class he attends. Alternately, he can get the second membership plan and pay

\$8

\$6

per class. If Evan attends a certain number of classes in a month, the two membership plans end up costing the same total amount. What is that total amount? How many classes per month is that?

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Each membership plan costs

\$\_\_\_\_\_

\_\_\_\_\_

classes per month.

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

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Lamar wrote a business plan for an entrepreneurship class, and now he has to make bound copies. Lamar could use a printer who charges a setup fee of

\$51

\$7

for every copy printed. Another possibility is to go to the office supply store, where he could pay an up-front fee of

\$24

\$8

per copy. There is a certain number of copies that makes the two options equivalent in terms of cost. How much would the copies cost? How many copies is that?

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\$

_____ for _____ copies.

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

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Two groups of workers are painting a bridge in the bay. The first group is responsible for painting the north side of the bridge, and the second group is responsible for painting the south side of the bridge. The first group has already painted

5

kilometers of the bridge and is painting

2

additional kilometers per day. The second group has already painted

2

kilometers of the bridge and is painting

3

additional kilometers per day. After a while, the two groups will have painted the same amount of the bridge. How long will that take? How much of the bridge will each group have painted?

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\_

days, both groups of workers will have painted

\_

kilometers of the bridge.

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

\newline

Mr. Sheppard, the owner of two car dealerships in Greenwood, is holding a contest to see which one can sell the most cars. Greenwood Cars has already sold

18

cars, and Sheppard's Autos has sold

20

cars. Going forward, the salespeople at Greenwood Cars think they can sell

9

cars per day, whereas the salespeople at Sheppard's Autos are aiming for sales of

8

cars per day. If the salespeople's predictions are accurate, it won't be long before the two dealerships are tied. How many cars will each lot have sold? How long will that take?

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The dealerships will each have sold

\_\_

\_\_

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