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Solve a system of equations using substitution

Solve the system of equations.

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\begin{array}{l} 7 x+10 y=36 \\ y=2 x+9 \\ x=\square \\ y=\square \end{array}

Solve the system of equations.

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\begin{array}{l} 12 x-5 y=-20 \\ y=x+4 \\ x=\square \\ y=\square \end{array}

Solve the system of equations.

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\begin{array}{l} -5 x+2 y=9 \\ y=7 x \\ x=\square \\ y=\square \end{array}

Solve the system of equations.

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\begin{array}{l} 10 x-9 y=24 \\ y=x-2 \\ x=\square \\ y=\square \end{array}

Solve the system of equations.

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\begin{array}{l} 7 x-3 y=20 \\ y=5 x-4 \\ x=\square \\ y=\square \end{array}

Solve the system of equations.

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\begin{array}{l} 8 x+5 y=24 \\ y=-4 x \\ x=\square \\ y=\square \end{array}

Solve the system of equations.

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\begin{array}{l} -5 x+4 y=3 \\ x=2 y-15 \\ x=\square \\ y=\square \end{array}

Solve the system of equations.

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\begin{array}{l} -10 x+3 y=5 \\ x=y-4 \\ x=\square \\ y=\square \end{array}

Solve the system of equations.

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\begin{array}{l} 15 x+31 y=-3 \\ x=-y+3 \\ x=\square \\ y=\square \end{array}

Solve the system of equations.

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\begin{array}{l} 3 x+4 y=-23 \\ x=3 y+1 \\ x=\square \\ y=\square \end{array}

Anya has two different sized cylindrical coffee mugs. The larger mug has an internal height of

15

(\mathrm{cm})

, and the smaller mug has an internal height of

10 \mathrm{~cm}

. Both mugs have an internal diameter of

8 \mathrm{~cm}

. Which of the following is closest to the difference in cubic centimeters

\left(\mathrm{cm}^{3}\right)

between the internal volume of the larger mug and the internal volume of the smaller mug?

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1

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63 \mathrm{~cm}^{3}

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251 \mathrm{~cm}^{3}

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754 \mathrm{~cm}^{3}

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1,005 \mathrm{~cm}^{3}

Akoni, a painter, painted a circular helicopter landing pad one color. Next she painted over a

3

meter radius circle in the center, in a different color. If the second coat of paint covered an area half the size of the first coat, which of the following is most nearly the radius of the landing pad?

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1

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2

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3

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4

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6

An architect has created a scale drawing for a residential townhouse in the shape of a rectangular prism. In the drawing, the internal width of the townhouse is labeled as

18

(\mathrm{ft})

, the internal length as

20 \mathrm{ft}

, and the internal height as

30 \mathrm{ft}

. The local building department tells the architect that if built, the building would be too tall according to local zoning laws and that its height must be reduced by

10 \%

. If the architect creates a second scale drawing where the townhouse's height is reduced by

10 \%

, what will be its new proposed internal volume in cubic feet?

468-6 g

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The volume of a rectangular birthday cake is

468

cubic inches. The expression above models the amount of cake remaining, in cubic inches, after serving

g

guests. How much cake, in cubic inches, would remain after serving

50

300-1.5 p

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To promote his new business, Claudio made

300

tamales to give to pedestrians. The expression above describes the number of tamales remaining after passing out samples to

p

pedestrians. If Claudio passed out samples to

160

pedestrians, how many tamales would remain?

5,500 P+4,500 S>50,000

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Huang Yi works as a paleontologist and a sculptor. She earns

\$ 5,500

per month as a paleontologist and

\$ 4,500

per month as a sculptor. Huang Yi wants to make more than

\$ 50,000

this year. In the given inequality,

P

represents the number of months Huang Yi can work as a paleontologist and

S

represents the number of months she can work as a sculptor to reach her goal. If Huang Yi worked for

6

months as a paleontologist this year, what is the minimum whole number of months that she must work as a sculptor to reach her goal?

\begin{array}{l} m+p=23 \\ m-7=p \end{array}

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The given system of equations relates

m

, the number of shirts Mara owns, and

p

, the number of shirts Phil owns. Which of the following is the best interpretation of the number

7

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1

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7

more shirts than Phil does.

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7

more shirts than Mara does.

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7

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7

A cable company with a reputation for poor customer service is losing subscribers at a rate of approximately

3 \%

per year. The company had

2

million subscribers at the start of

2014

. Assume that the company continues to lose subscribers at the same rate, and that there are no new subscribers. Which of the following functions,

S

, models the number of subscribers (in millions) remaining

t

years after the start of

2014

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1

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S(t)=2(1.03)^{t}

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S(t)=2(0.97)^{t}

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S(t)=2(0.70)^{t}

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S(t)=2(0.97) t

Two climate scientists are creating models for global rising sea levels. One scientist proposes a

10

-year doubling model, which predicts that the change in sea level,

R(t)

, will grow according to the following function:

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R(t)=\frac{125}{256} \cdot(2)^{\frac{t}{10}}

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t

is the number of years after

2005

. The other scientist proposes a steady increase model where the change in sea level will increase by

5

(\mathrm{cm})

per year. Both models predict that in the year

2105

, the sea level will increase by

500 \mathrm{~cm}

. To the nearest centimeter, how much greater is the predictions of the steady increase model than the

10

-year doubling model for the change in sea level in the year

2055

h(t)=-4.9 t^{2}+18 t+0.5

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The equation models

h

, the height, in meters, of a soccer ball

t

seconds after the goalkeeper kicks it. Which of the following statements is the best interpretation of the ordered pair

(3,10.4)

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1

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3

seconds after the kick, the distance between the soccer ball and the goalkeeper is

10

4

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3

seconds after the kick, the soccer ball is traveling at a speed of

10

4

meters per second.

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3

seconds after the kick, the height of the soccer ball is

10

4

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10

4

seconds after the kick, the height of the soccer ball is

3

Solve the system of equations.

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\begin{array}{l} 6 x-5 y=15 \\ x=y+3 \\ x=\square \\ y=\square \end{array}

3

years older than Daniel. Two years ago, Kevin was

4

times as old as Daniel.

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k

be Kevin's age and let

d

be Daniel's age.

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Which system of equations represents this situation?

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1

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\left\{\begin{array}{l}k=d+3 \\ k-2=4(d-2)\end{array}\right.

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\left\{\begin{array}{l}k-2=(d-2)+3 \\ k=4 d\end{array}\right.

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\left\{\begin{array}{l}d-2=(k-2)+3 \\ d=4 k\end{array}\right.

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\left\{\begin{array}{l}d=k+3 \\ d-2=4(k-2)\end{array}\right.

P=\frac{19}{2}+\frac{4}{25} d

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The amount of paint,

P

, in pints, that an art studio can buy with

d

dollars is given by the equation. What is the best interpretation of

\frac{4}{25}

as shown in the equation?

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1

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(A) The paint costs

\frac{4}{25}

of a dollar per pint.

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(B) One dollar can buy

\frac{4}{25}

of a pint of paint.

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(C) The art studio started with

\frac{4}{25}

of a pint of paint.

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(D) The art studio can purchase at most

\frac{4}{25}

of a pint of paint.

P=67,000+2,820 m

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The total payments,

P

, in dollars, made by a homeowner

m

months after starting payments on a home mortgage is given by the equation. What is the best interpretation of

67

000

as shown in the given equation?

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1

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A The first payment was

67

000

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(B) The homeowner pays

67

000

dollars each month.

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(C) The homeowner paid

67

000

dollars at the end of the first month.

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D The total of all payments made by the homeowner is

67

000

C=16,500+130 m

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The total cost,

C

, in dollars, to purchase a planchet machine and use it for

m

months is given by the equation. What is the best interpretation of

130

as shown in the given equation?

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1

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(A) The cost increase by

130

dollars for each additional month of use.

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B The cost to purchase the machine and not use it is

130

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(C) After purchase, the machine can be used for up to

130

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D) The average cost per month to purchase and use the machine is

130

Today, the population of Canyon Falls is

22

500

and the population of Swift Creek is

15

200

. The population of Canyon Falls is decreasing at the rate of

740

people each year while the population of Swift Creek is increasing at the rate of

1

500

people each year. Assuming these rates continue into the future, in how many years from today will the population of Swift Creek equal twice the population of Canyon Falls?

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1

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9

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10

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11

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12

A company produces candy bags that each hold about

528

cubic inches of candy. Each bag is filled with any mixture of lollipop candies and gummy bear candies. When a bag contains only lollipop candies, then it has about

361

candies. When a bag contains only gummy bear candies, then it has about

697

candies. Given any candy bag produced by this company, which of the following equations could relate the approximate number of lollipop candies,

l

, in the bag and the approximate number of gummy bear candies,

g

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1

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\frac{l}{361}+\frac{g}{697}=528

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361 l+697 g=528

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\frac{l}{361}+\frac{g}{697}=1

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361 l+697 g=1

A jar of jelly bean candies weighs

8

ounces. A container of caramel candies weighs

40

ounces. Lúcia buys

10

pounds worth of jelly bean candy jars and caramel candy containers for her big party. Given that there are

16

ounces in a pound, which of the following equations correctly relates the number of jars of jelly bean candies,

j

, and the number of containers of caramel candies,

c

, that Lúcia bought?

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1

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\frac{8}{16} j+\frac{40}{16} c=10

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8 j+40 c=10

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\frac{16}{8} j+\frac{16}{40} c=10

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16 \cdot 8 j+16 \cdot 40 c=10

C=1,500 n+1,000

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C

, in dollars, to ship

n

cars from Europe to the United States is given in the equation. What is the difference, in cost, to ship

7

6

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1

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\$ 500

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\$ 1,000

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\$ 1,500

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\$ 2,500

Jelani needs to hire at least

12

artists for an upcoming event. He needs to hire visual artists, who will be paid

\$ 300

for the event, and performers, who will be paid

\$ 480

for the event. His budget for paying the artists is no more than

\$ 6,000

. He must hire at least

4

visual artists and at least

3

performers. Which of the following does not satisfy all of the conditions described?

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1

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4

visual artists and

10

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8

visual artists and

8

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9

visual artists and

3

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13

visual artists and

4

A rectangular garden has a length of

60

\mathrm{ft}

w

\mathrm{ft}

, and a perimeter of

200

\mathrm{ft}

. Which of the following equations best models the garden's perimeter?

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1

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60+w=200

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60+2 w=200

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120+w=200

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120+2 w=200

A grocery store sells

5

-pound bags of beans for

\$ 6

10

-pound bags of rice for

\$ 15

each. Taye wants to buy at least as many pounds of rice as he buys of beans. He wants to spend at least

\$ 60

, and he can carry a maximum of

55

pounds. Which of the following purchases satisfies all of Taye's conditions?

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1

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3

bags of beans and

6

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4

bags of beans and

2

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4

bags of beans and

3

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6

bags of beans and

2

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

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Last Wednesday, two friends met up after school to read the book they were both assigned in Literature class. Bryan can read

2

pages per minute, and he had already read

98

pages. Jayla, who has a reading speed of

3

pages per minute, had read

48

pages. Eventually they had read the same number of pages. How long did that take? How many pages had each of them read?

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\_\_\_\_

minutes, Bryan and Jayla had each read

\_\_\_\_

Solve using substitution.

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y = -5

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-4x + 3y = 17

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