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Solve a system of equations using any method

A fashion photographer needs to hire a stylist to prepare her models. Gina charges

\$200

for showing up, plus

\$60

per hour. Kendra charges

\$150

\$70

per hour. The photographer realizes that, given the expected duration of her photo shoot, either stylist would cost her the same amount. What would the duration be?

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Write a system of equations, graph them, and type the solution.

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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. Two classmates got together over the weekend to do their assigned History reading. Oscar can read

1

page per minute, while Luther can read

4

pages per minute. When they met, Oscar had already read

53

pages, and Luther had already gotten through

23

pages. After a while, they had both read the same number of pages. How long did that take? How many pages had each one read? After

t

minutes, Oscar and Luther had each read

p

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x = 2

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-9x - 6y = 6

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-4x - y = 1

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y = 3

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y = -1

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-9x - 3y = 12

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x = -7

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-3x - 7y = -14

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x = -3

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-6x + 6y = -6

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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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Two coworkers picked up some writing instruments at the office supply store. Olivia selected

1

box of pencils, paying

\$2

. Next, Grayson spent

\$18

6

boxes of pencils and

2

boxes of ballpoint pens. How much does a box of each cost?

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A box of pencils costs

\$\_\_\_\_

, and a box of pens costs

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Evie stopped exercising

4

months ago due to an injury. Since she stopped exercising, she has lost

1 \frac{1}{2}

kilograms of muscle mass per month.

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The following equation describes this situation:

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-1 \frac{1}{2} \cdot 4=-6

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-6

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1

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6

kilograms of muscle mass each month.

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(B) Evie gained a total of

6

kilograms of muscle mass.

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(C) Evie lost a total of

6

kilograms of muscle mass.

A certain reality TV show lost a total of

9

000

viewers over the past

3

months. It lost the same number of viewers each month.

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The following equation describes this situation.

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-9,000 \div 3=-3,000

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-3,000

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1

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3

000

fewer people watching the show compared to three months ago.

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(B)The total change in the number of people watching the show is

-3,000

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(C) The loss in the number of people watching the show each month was

3

000

Ming is training for a

10 \mathrm{~K}

run. For each of her last

4

training runs, she reduced her time

2

5

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The following equation describes this situation:

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4 \cdot(-2.5)=-10

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-10

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1

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(A) Ming's distance decreased a total of

10

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(B) Ming's run time decreased a total of

10

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(C) Ming's run time increased a total of

10

Jared lost a total of

\$ 9.00

on his investment over

2

months. He lost an equal amount of money each month.

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The following equation describes this situation.

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-9.00 \div 2=-4.50

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-4

50

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1

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(A) Jared's investment was worth

\$ 4.50

less than it was two months ago.

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(B) The loss in value on Jared's investment each month was

\$ 4.50

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(C) The total change in Jared's

Keone is driving cross-country. The engine burns

7.5 \mathrm{~L}

100 \mathrm{~km}

. So far, they burned

37.5 \mathrm{~L}

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The following equation describes this situation.

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-37.5 \div-7.5=5

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5

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1

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(A) Keone has driven for

5

hundred kilometers.

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(B) Keone has driven for

5

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(C) Keone can drive

5 \mathrm{~km}

per liter of fuel.

Akash's cell phone bill was

\$ 79.99

3

months. His payments came out of his checking account each month.

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The following equation describes this situation.

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-79.99 \cdot 3=-239.97

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-239

97

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1

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A The total change in Akash's checking account as a result of these

3

cell phone bills was

\mathbf{-} \$ 239.97

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(B) Each month, Akash paid

\$ 239.97

from his checking account for his cell phone.

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\$ 239.97

left in Akash's checking account.

Solve using augmented matrices.

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-7x - 7y = 14

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x = -8

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Solve each word problem by finding GCF or LCM.

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Pencils come in packages of

10

. Erasers come in packages of

12

. Phillip wants to purchase the smallest number of pencils and erasers so that he will have exactly

1

eraser per pencil. How many packages of pencils and erasers should Phillip buy?

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4

packages of pencils and

3

packages of erasers

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5

packages of pencils and

4

packages of erasers

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6

packages of pencils and

5

packages of erasers

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12

packages of pencils and

10

packages of erasers

Pencils come in packages of

10

. Erasers come in packages of

12

. Philip wants to purchase the smallest number of pencils and erasers so that he will have exactly

1

eraser per pencil. How many packages of pencils and erasers should Phillip buy?

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

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Mrs. Moore is researching what it would cost to order flower arrangements for a fancy party. She wants one large centerpiece for the head table, and smaller arrangements for the smaller tables. Bloomington Florist charges

\$10

for each smaller arrangement, plus

\$45

for the large centerpiece. Quincy's Flowers, in contrast, charges

\$47

for the large centerpiece and

\$9

per arrangement for the rest. If Mrs. Moore orders a certain number of small arrangements, the cost will be the same at either flower shop. How many small arrangements would that be? What would the total cost be?

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If Mrs. Moore orders _____ small arrangements, it will cost

\$

_____ at either shop.

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

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Dr. Thompson, a pediatrician, has

3

annual checkups and

2

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

220

minutes on his schedule. Next Wednesday, he has

3

annual checkups and

3

sick visits on the schedule, which should take

246

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

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The time allotted is

\_

minutes for an annual checkup and

\_

minutes for a sick visit.

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

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Kirk is going to send some flowers to his wife. Lakeside Florist charges

\$1

\$36

for the vase. Colette's Flowers, in contrast, charges

\$2

\$10

for the vase. If Kirk orders the bouquet with a certain number of roses, the cost will be the same with either flower shop. How many roses would there be? What would the total cost be?

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If the bouquet contains

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roses, it will cost

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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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Dr. Yamamoto, a pediatrician, has

3

annual checkups and

1

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

159

minutes on his schedule. Next Wednesday, he has

1

annual checkup and

1

sick visit on the schedule, which should take

63

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

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The time allotted is

\_

minutes for an annual checkup and

\_

minutes for a sick visit.

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

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Denise plans to attend the Boone County Fair and is trying to decide what would be a better deal. She can pay

\$36

for unlimited rides, or she can pay

\$15

for admission plus

\$3

per ride. If Denise goes on a certain number of rides, the two options wind up costing her the same amount. How many rides is that? What is that cost?

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If Denise goes on _____ rides, the two options will 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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Gavin flew home from vacation with a heavy bag. With the first airline he flew, Gavin had to pay

\$18

to check his bag, plus

\$12

for every kilogram that his bag was over the weight limit. The next flight was with another airline that had the same weight limit. Gavin had to pay

\$11

per kilogram that his bag was over the weight limit, in addition to the checked bag fee of

\$23

. By coincidence, the fees ended up being the same with both airlines. How far over the weight limit was the bag? How large was each airline's fee?

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The bag was ___ kilograms over the weight limit, and each airline's fee was

\$

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

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Wayne and Eddie got in trouble at football practice and have to run laps as a consequence. Wayne, who runs at a rate of

3

laps per minute, had completed

12

laps already when he was joined on the track by Eddie. Eddie's pace is

4

laps per minute. At some point, the two will have run the same distance. How many laps will each boy have run? How long will that take?

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Wayne and Eddie will each have run

\_

\_

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

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For her parents' anniversary party, Maddie is considering using one of two venues. A hotel in Springfield will cost

\$269

for a reservation, plus

\$28

per person. A restaurant in the same city will cost

\$30

per person, in addition to

\$267

for the reservation. In order to make the best decision, Maddie figures out how many attendees it would take to have the venues cost the same amount. How many attendees would that be? What would the total cost be?

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If the party had _____ attendees, the cost at each venue would be

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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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Nina and Jerry are comparing the international calling plans on their cell phones. On her plan, Nina pays

\$2

just to place a call and

\$4

for each minute. When Jerry makes an international call, he pays

\$4

to place the call and

\$2

for each minute. A call of a certain duration would cost exactly the same under both plans. What is the duration? What is the cost?

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A call of _____ minutes would cost

\$

_____ under each plan.

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

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A TV station executive is planning the new lineup for next season's shows. On Monday nights, there will be

6

5

dramas, for a total of

416

minutes of programming, not counting commercials. On Tuesday nights, he has scheduled

5

5

dramas, for a total of

390

minutes of non-commercial programming. All sitcoms have the same length and all dramas have the same length. How long is each type of show?

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\_

minutes long and dramas are

\_

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

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Sparkles the Clown makes balloon animals for children at birthday parties. At Aubrey's party, he made

4

balloon poodles and

4

balloon giraffes, which used a total of

20

balloons. For Josie's party, he used

13

balloons to make

5

balloon poodles and

1

balloon giraffe. How many balloons does each animal require?

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Each poodle requires _____ balloons and each giraffe requires _____ balloons.

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8x - 8y = -16

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y = 5

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-5x + 5y = 10

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y = 4

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-3x - 3y = -18

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x = 2

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-4x + 2y = -14

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x = 5

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-8x + 10y = 2

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x = 6

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-5x - 6y = 5

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y = 5

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-4x + 8y = -4

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x = -1

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-6x - 10y = -2

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y = 5

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-7x - 7y = 14

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y = 5

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-3x - 3y = 9

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x = 2

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-3x + 2y = -18

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x = 10

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-9x + 6y = -15

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x = 5

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-3x - 6y = -15

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x = 7

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-5x - 5y = -15

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x = 7

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x = -9

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-4x + 5y = -14

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10x - 7y = -1

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x = 2

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-x - 7y = -11

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y = 1

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y = 4

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9x + 4y = 7

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-x - 9y = 13

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x = 5

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x = 5

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5x + 5y = 15

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x = 3

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-10x - 3y = -15

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y = 4

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–5x + 10y = 15

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...