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Solve a system of equations using elimination

In which story could you use the quotient

-15 \div -3

to answer the question?

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Choices:

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(A)To pass time in the car, Victoria and her sister create a game. Each person picks a side of the road to watch and calculates a score from the road signs. Green signs are worth

2

points, and white signs are worth

-3

points. If Victoria sees no green signs and

15

white signs, what is her final score?

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(B)To pass time in the car, Victoria and her sister create a game. Each person picks a side of the road to watch and calculates a score from the road signs. Green signs are worth

2

points, and white signs are worth

-3

points. If Victoria sees no green signs and ends with a score of

-15

, how many white signs does she see?

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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks. Erica gets paid at home for doing extra chores. Last week, she did

2

loads of laundry and

8

loads of dishes, and her parents paid her

\$14

. The week before, she finished

1

load of laundry and

8

loads of dishes, earning a total of

\$11

. How much does Erica earn for completing each type of chore? Erica earns

\$\_\_\_\_

per load of laundry and

\$\_\_\_\_

per load of dishes.

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

\newline

The owner of a new restaurant is designing the floor plan, and he is deciding between two different seating arrangements. The first plan consists of

15

tables and

20

booths, which will seat a total of

205

people. The second plan consists of

25

tables and

25

booths, which will seat a total of

275

people. How many people can be seated at each type of table?

\newline

Every table can seat

\_

people, and every booth can seat

\_

people.

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

\newline

At a historical landmark, candles are used to simulate an authentic atmosphere. A volunteer is currently putting new candles in the candle holders. On the east side, he replaced candles in

7

small candle holders and

3

large candle holders, using a total of

39

candles. On the west side, he replaced the candles in

23

small candle holders and

7

large candle holders, for a total of

111

candles. How many candles does each candle holder hold?

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Each small candleholder holds

\_

candles, and each large one holds

\_

candles.

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

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The Bloomington High School Science Department is purchasing new earth science and physics textbooks this year. Ms. Sheppard has requested

77

earth science textbooks and

85

physics textbooks for all of her classes, which costs the department a total of

\$8,998

. Mr. Blackburn has asked for

77

earth science textbooks and

87

physics textbooks, which will cost a total of

\$9,130

. How much do the textbooks cost?

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Earth science textbooks cost

\$

_____ apiece and physics textbooks cost

\$

_____ apiece.

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

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Farid received some gift cards for music and movie downloads for his birthday. Using one of them, he downloaded

12

songs and

18

movies, which cost a total of

\$186

. Using another, he purchased

18

songs and

15

movies, which cost a total of

\$171

. How much does each download cost?

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Downloads cost

\$\_

for a song and

\$\_

for a movie.

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

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Lowell City Cafe recently introduced a new flavor of coffee. They served

67

grande cups and

36

jumbo cups of the new coffee today, which equaled a total of

48,781

grams. The day before,

67

grande cups and

64

jumbo cups were served, which used a total of

65,721

grams. How much coffee is required to make each size?

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There are

\_

grams in a grande cup of coffee and

\_

grams in a jumbo one.

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

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Emily owns a cake shop and she is working on two wedding cakes this week. The first cake consists of

4

small tiers and

4

large tiers, which will serve a total of

268

guests. The second one includes

2

small tiers and

4

large tiers, which is enough servings for

228

guests. How many guests does each size of tier serve?

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A small tier will serve

\_

guests and a large tier will serve

\_

guests.

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

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Eli gets paid at home for doing extra chores. Last week, he did

8

loads of laundry and

3

loads of dishes, and his parents paid him

\$35

. The week before, he finished

8

loads of laundry and

6

loads of dishes, earning a total of

\$38

. How much does Eli earn for completing each type of chore?

\newline

Eli earns

\$

_____ per load of laundry and

\$

_____ per load of dishes.

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

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The members of a sewing circle are making blankets to give to shelters. This week, they made

14

twin-size blankets and

27

queen-size blankets, using a total of

284

yards of fabric. Last week, the members completed

47

twin-size blankets and

45

queen-size blankets, which required

497

total yards of fabric. How much fabric is used for the different sizes of blankets?

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A twin-size blanket uses

\_

yards of fabric and a queen-size one uses

\_

yards.

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Write a system of equations to describe the situation below, solve using an augmented matrix, and fill in the blanks.

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Andy loves riding Ferris wheels and roller coasters. While visiting the Morgan County Fair, he first went on the Ferris wheel

1

time, using a total of

2

tickets. Then, after taking a break and having a snack, Andy went on the Ferris wheel

2

times and the roller coaster

4

times, using a total of

20

tickets. How many tickets does it take to ride each attraction?

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It takes

\_\_\_\_

tickets to ride the Ferris wheel, and

\_\_\_\_

tickets to ride the roller coaster.

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

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A boutique in Winchester specializes in leather goods for men. Last month, the company sold

10

wallets and

35

belts, for a total of

\$1,450

. This month, they sold

77

wallets and

21

belts, for a total of

\$3,710

. How much does the boutique charge for each item?

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The boutique charges

\$\_\_\_\_

for a wallet, and

\$\_\_\_\_

for a belt.

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

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Nora wanted to stock up on drinks for an upcoming party. First, she spent

\$60

15

cases of juice and

15

cases of soda, which is all the store had in stock. A few days later, she returned to the store and purchased an additional

5

cases of juice and

9

cases of soda, spending a total of

\$28

. What is the price of each drink?

\newline

The price for a case of juice is

\$

____, and the price for a case of soda is

\$

____

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

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The box office at a theater is selling tickets for a series of rock concerts. So far, they have sold

94

balcony tickets and

99

general admission floor tickets for Friday's show, for a total of

\$7,660

in receipts. For Saturday's show,

61

balcony tickets and

59

general admission floor tickets have been sold, equaling

\$4,824

in receipts. How much does each ticket cost?

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A balcony seat ticket costs _____, and a general admission floor ticket costs

\$

_____.

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

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A realtor is decorating some homes for sale, putting a certain number of decorative pillows on each twin bed and a certain number on each queen bed. In one house, she decorated

4

twin beds and

1

queen bed and used a total of

34

pillows. At another house, she used

76

pillows to spruce up

4

twin beds and

4

queen beds. How many decorative pillows did the realtor arrange on each bed?

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The realtor used

\_\_\_\_

pillows on every twin bed and

\_\_\_\_

pillows on every queen bed.

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

\newline

At a historical landmark, candles are used to simulate an authentic atmosphere. A volunteer is currently putting new candles in the candle holders. On the east side, he replaced candles in

7

small candle holders and

3

large candle holders, using a total of

45

candles. On the west side, he replaced the candles in

19

small candle holders and

19

large candle holders, for a total of

209

candles. How many candles does each candle holder hold?

\newline

Each small candleholder holds

\_

candles, and each large one holds

\_

candles.

Get tutor help

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

\newline

The members of a sewing circle are making blankets to give to shelters. This week, they made

14

twin-size blankets and

48

queen-size blankets, using a total of

440

yards of fabric. Last week, the members completed

32

twin-size blankets and

12

queen-size blankets, which required

224

total yards of fabric. How much fabric is used for the different sizes of blankets?

\newline

A twin-size blanket uses

\_

yards of fabric and a queen-size one uses

\_

yards.

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

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To keep in shape, Dillon exercises at a track near his home. He requires

50

minutes to do

10

laps running and

5

laps walking. In contrast, he requires

47

minutes to do

9

laps running and

5

laps walking. Assuming he maintains a consistent pace while running and while walking, how long does Dillon take to complete a lap?

\newline

Dillon takes

\_

minutes to run a lap and

\_

minutes to walk a lap.

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

\newline

Trisha loves riding Ferris wheels and roller coasters. While visiting the Scott County Fair, she first went on the Ferris wheel

1

time and the roller coaster

1

time, using a total of

6

tickets. Then, after taking a break and having a snack, Trisha went on the Ferris wheel

4

times and the roller coaster

2

times, using a total of

16

tickets. How many tickets does it take to ride each attraction?

\newline

It takes

\_

tickets to ride the Ferris wheel, and

\_

tickets to ride the roller coaster.

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

\newline

The members of a sewing circle are making blankets to give to shelters. This week, they made

44

twin-size blankets and

35

queen-size blankets, using a total of

526

yards of fabric. Last week, the members completed

23

twin-size blankets and

35

queen-size blankets, which required

442

total yards of fabric. How much fabric is used for the different sizes of blankets?

\newline

A twin-size blanket uses

\_

yards of fabric and a queen-size one uses

\_

yards.

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

\newline

Dr. Harvey, a pediatrician, has

2

annual checkups and

3

sick visits scheduled next Tuesday, which will fill a total of

190

minutes on her schedule. Next Wednesday, she has

1

annual checkup and

3

sick visits on the schedule, which should take

140

minutes. How much time is allotted for each type of appointment?

\newline

The time allotted is

\_

minutes for an annual checkup and

\_

minutes for a sick visit.

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

\newline

Emma likes to knit hats and mittens for friends and family. Last fall, she knitted

1

hat and

3

pairs of mittens, which took a total of

46

hours. This fall, she knitted

1

hat and

1

pair of mittens, which took a total of

18

hours. If each hat takes the same amount of time and each pair of mittens takes the same time, how long does it take Emma to knit each item?

\newline

It takes Emma

\_

hours to knit a hat and

\_

hours to knit a pair of mittens.

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

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Friends and family of the bride will be helping assemble centerpieces for the wedding reception. On the right side of the room, there will be

1

round table and

3

rectangular tables, which will require a total of

10

centerpieces. On the left side, there will be

15

round tables and

2

rectangular tables, for which they will need to assemble a total of

21

centerpieces. How many centerpieces will be on each table?

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There will be _____ centerpieces on every round table and _____ centerpieces on every rectangular one.

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

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One Friday night, two large groups of people called Princeton Taxi Service. The first group requested

1

sedan and

2

minivans, which can seat a total of

15

people. The second group asked for

2

sedans and

3

minivans, which can seat a total of

24

people. How many passengers can each type of taxi seat?

\newline

A sedan can seat

\_

people, and a minivan can seat

\_

people.

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

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Two brothers went shopping at a back-to-school sale where all shirts were the same price, and all the shorts too. The younger brother spent

\$131

9

new shirts and

4

pairs of shorts. The older brother purchased

9

new shirts and

5

pairs of shorts and paid a total of

\$148

. How much did each item cost?

\newline

Each shirt cost

\$\_\_\_\_

, and each pair of shorts cost

\$\_\_\_\_

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

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One Friday night, two large groups of people called Sparrowtown Taxi Service. The first group requested

1

sedan and

1

minivan, which can seat a total of

10

people. The second group asked for

3

sedans and

1

minivan, which can seat a total of

18

people. How many passengers can each type of taxi seat?

\newline

A sedan can seat _____ people, and a minivan can seat _____ people.

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

\newline

An online boutique is having a special on personalized baby items. On Monday, they sold

12

personalized baby blankets and

11

personalized hooded towels, for a total of

\$569

in receipts. The following day, they received orders for

1

personalized baby blanket and

11

personalized hooded towels, which brought in a total of

\$239

. How much does each item sell for?

\newline

Blankets sell for

\$

_____ apiece, and hooded towels sell for

\$

_____ apiece.

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

\newline

An employee at a company that assembles chandeliers is packing boxes for shipping. In the first box, he packed

1

small chandelier and

4

large chandeliers, which weighed a total of

207

pounds. In the second box, he packed

4

small chandeliers and

1

large chandelier, which had a weight of

93

pounds. Assuming the weight of the box isn't included in the shipping weight, how much does each size of chandelier weigh?

\newline

Each small chandelier weighs

\_

pounds and each large one weighs

\_

pounds.

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

\newline

Billy gets paid at home for doing extra chores. Last week, he did

4

loads of laundry and

2

loads of dishes, and his parents paid him

\$10

. The week before, he finished

6

loads of laundry and

7

loads of dishes, earning a total of

\$19

. How much does Billy earn for completing each type of chore?

\newline

Billy earns

\$\_\_\_\_

per load of laundry and

\$\_\_\_\_

per load of dishes.

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

\newline

Colleen loves riding Ferris wheels and roller coasters. While visiting the Butler County Fair, she first went on the Ferris wheel

4

times and the roller coaster

2

times, using a total of

18

tickets. Then, after taking a break and having a snack, Colleen went on the Ferris wheel

4

times and the roller coaster

4

times, using a total of

28

tickets. How many tickets does it take to ride each attraction?

\newline

It takes

\_

tickets to ride the Ferris wheel, and

\_

tickets to ride the roller coaster.

Get tutor help

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

\newline

The owner of a new restaurant is designing the floor plan, and he is deciding between two different seating arrangements. The first plan consists of

18

tables and

20

booths, which will seat a total of

290

people. The second plan consists of

20

tables and

25

booths, which will seat a total of

350

people. How many people can be seated at each type of table?

\newline

Every table can seat

\_

people, and every booth can seat

\_

people.

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

\newline

A librarian is expanding some sections of the city library. He buys books at a special price from a dealer who charges one price for any hardback book and another price for any paperback book. For the children's section, Mr. Hatfield purchased

24

new hardcover books and

37

new paperback books, which cost a total of

\$303

. He also purchased

24

new hardcover books and

96

new paperback books for the adult fiction section, spending a total of

\$480

. What is the special price for each type of book?

\newline

The special price is

\$\_

for hardcover books and

\$\_

for paperback books.

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

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Julia is thinking of two numbers. Adding

6

times the first number and

3

times the second number gives a total of

18

. Also, adding

6

times the first number and

10

times the second number gives

4

. What are the two numbers?

\newline

The first number is _____, and the second number is _____.

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

\newline

At a community barbecue, Mrs. Davidson and Mr. Ayala are buying dinner for their families. Mrs. Davidson purchases

2

hot dog meals and

3

hamburger meals, paying a total of

\$39

. Mr. Ayala buys

3

hot dog meals and

3

hamburger meals, spending

\$45

in all. How much do the meals cost?

\newline

Hot dog meals cost

\$

_____ each, and hamburger meals cost

\$

_____ each.

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

\newline

Jordan and Donald went to an arcade where the machines took tokens. Jordan played

1

game of skee ball and

7

games of pinball, using a total of

23

tokens. At the same time, Donald played

2

games of skee ball and

3

games of pinball, using up

13

tokens. How many tokens does each game require?

\newline

Every game of skee ball requires

\_

tokens, and every game of pinball requires

\_

tokens.

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

\newline

A coffee shop is having a sale on prepackaged coffee and tea. Yesterday they sold

10

packages of coffee and

31

packages of tea, for which customers paid a total of

\$204

. The day before,

10

packages of coffee and

47

packages of tea was sold, which brought in a total of

\$268

. How much does each package cost?

\newline

Per package, coffee costs

\$

_____ and tea costs

\$

_____.

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

\newline

An employee at a company that assembles chandeliers is packing boxes for shipping. In the first box, he packed

4

small chandeliers and

2

large chandeliers, which weighed a total of

66

kilograms. In the second box, he packed

4

small chandeliers and

4

large chandeliers, which had a weight of

112

kilograms. Assuming the weight of the box isn't included in the shipping weight, how much does each size of chandelier weigh?

\newline

Each small chandelier weighs

\_

kilograms and each large one weighs

\_

kilograms.

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

\newline

Beth is creating beaded jewelry to give to her family and friends. For her family, she assembled

2

bracelets and

5

necklaces, using a total of

370

beads. For her friends, she assembled

7

bracelets and

5

necklaces, using a total of

595

beads. Assuming she uses a consistent number of beads for every bracelet and necklace, how many beads is she using for each?

\newline

Beth uses

\_

beads for each bracelet and

\_

beads for each necklace.

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

\newline

There are two mystery numbers. The sum of

10

times the first number and

10

times the second number is

-20

. The sum of

10

times the first number and

6

times the second number is

-4

. What are the two numbers?

\newline

The first number is _____, and the second number is _____.

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

\newline

The owner of Summerfield Florist is assembling flower arrangements for Valentine's Day. This morning, she assembled

6

small arrangements and

8

large arrangements, which took her a total of

92

minutes. After lunch, she arranged

5

small arrangements and

12

large arrangements, which took

130

minutes. How long does it take to assemble each type?

\newline

The florist can assemble a small arrangement in

\_

minutes and a large one in

\_

minutes.

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

\newline

A coffee shop is having a sale on prepackaged coffee and tea. Yesterday they sold

25

packages of coffee and

39

packages of tea, for which customers paid a total of

\$587

. The day before,

10

packages of coffee and

39

packages of tea was sold, which brought in a total of

\$422

. How much does each package cost?

\newline

Per package, coffee costs

\$\_\_\_\_

and tea costs

\$\_\_\_\_

Get tutor help

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

\newline

Carmen likes to make desserts for bake sales. Last month, she made

3

batches of brownies and

3

batches of cookies, which called for

18

eggs total. The month before, she baked

3

batches of brownies and

1

batch of cookies, which required a total of

10

eggs. How many eggs did Carmen use for a batch of each dessert?

\newline

Carmen uses

\_

eggs to make a batch of brownies and

\_

eggs to make a batch of cookies.

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Simplify.

\newline

\frac{2}{3} c-\frac{1}{5} c

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What is the result of subtracting the second equation from the first?

\newline

\begin{array}{l} 2 x+7 y=-8 \\ 2 x-5 y=-1 \end{array}

\newline

\square

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What is the result of adding these two equations?

\newline

5 x-y=6

\newline

-2 x+y=8

\newline

\square

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What is the result of subtracting the second equation from the first?

\newline

-2 x+y=0

\newline

-7 x+3 y=2

\newline

\square

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What is the result of adding these two equations?

\newline

\begin{array}{c} 2 x+7 y=4 \\ -2 x-8 y=-2 \end{array}

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What is the result of adding these two equations?

\newline

\begin{array}{c} 5 x-9 y=1 \\ -7 x+2 y=-5 \end{array}

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What is the result of adding these two equations?

\newline

\begin{aligned} 4 x-4 y & =-2 \\ -9 x-4 y & =-3 \end{aligned}

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Solve the system of equations.

\newline

\begin{array}{l} 11 x+4 y=-46 \\ 7 x-4 y=10 \\ x=\square \\ y=\square \end{array}

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