10-1B Lesson Master - North Hunterdon-Voorhees Regional ... · Two people paddle a canoe 8 miles upstream in two hours. Then they turn around and paddle 8 miles downstream in one

440 Algebra

Name

Copyr

ight

© W

right

Gro

up/M

cG

raw

-Hill

Questions on SPUR ObjectivesSee pages 650–653 for objectives.

Lesson Master

REPRESENTATIONS Objective I

1. Refer to the graph at the right.

a. What system is represented?

b. What is the solution?

c. Verify your answer to part b.

2. Refer to the graph at the right.

a. What system is represented?

b. What is the solution?

c. Verify your answer to part b.

In 3–5, a system is given. Solve the system by graphing.

3. y - 3x = −4

y = 2x - 1

4. 3x + 6y = 0

y = 4x + 9

5. 2x - 6y = −5

y = 4x −1

10-1B

x

y

1-1-2-3-4-5-6-7-8

1

-1

-2

-3

-4

-5

-6

-7

-8

2

4

5

6

7

8

2 3 4 5 6 7 8

x

y

1-1-2-3-4-5-6-7-8

1

-1

-2

-3

-4

-5

-6

-7

-8

2

4

5

6

7

8

9

10

3 4 5 6 7 8

x

y

x

y

x

y

Back to Lesson 10-1 Answer Page

Algebra 441

Name

Copyrig

ht ©

Wrig

ht G

roup/M

cG

raw

-Hill

page 210-1B

In 6–8, a system is given. Solve the system by graphing.

6. y = 4x + 14

y = 2x + 10

7. y = −x + 7

y = 1 __

2 x + 1

8. 3x - 4y = 3

4y = x -9

In 9 and 10, a situation is described. a. Translate the information into two equations. b. Use a

calculator table to ! nd a good window to display the graph. What window did you use? c. Use the

graph from Part b to answer the question.

9. A coin jar contains only nickels and quarters. There are exactly 38 coins

in the jar, and the total value of the coins is $2.50.

a. Let x = the number of nickels in the jar.

Let y = the number of quarters in the jar.

b.

c. How many of each kind of coin is in the jar?

10. A tomato plant 6 centimeters tall is growing at a rate of 4 centimeters

per day. Another tomato plant 10 centimeters tall is growing at a rate of

2 centimeters per day.

a. Let x = the number of days the plant has been growing.

Let y = the height of the plant after x days.

b.

c. After how many days will the plants be the same height?

How tall will they be?

x

y

x

y

x

y

SMP08ALG_NA_TR2_C10.indd 441 5/31/07 10:46:04 AM


Algebra 443

Name

Copyrig

ht ©

Wrig

ht G

roup/M

cG

raw

-Hill

Lesson Master10-2B

SKILLS Objective A

In 1–8, a system is given. Use substitution to ! nd the solution.

1. y = 3x

y = −x + 4

2. b = 2a + 5

b = a + 3

3. y = 3x + 1

y = 0.5x - 4

4. y = 2x - 5

y = −2x + 7

5. y = 1 __

2 x

y = 3x + 4 6.

d = 1 __ 3 c + 7

d = 2 __ 3 c + 8

7. y = 1 __

2 x + 5

y = −4x - 4 8.

y = 0.4

y = 0.2x + 6



444 Algebra

Name

Copyr

ight

© W

right

Gro

up/M

cG

raw

-Hill

page 2

USES Objective G

9. Carl is 0.2 mile ahead of Andrea on his bicycle. Andrea rides at 15 mph

on the same road trying to catch up to him. Carl rides at a rate of 10

mph. Their father is also riding his bike on the same road and reaches

Andrea in 5 minutes. Solve a system of equations to fi nd out if their

father reaches Andrea before she catches up to Carl.

10. Car rental A costs $20 per day and $0.10 per mile and care rental B

costs $15 per day and $0.20 per mile. Solve a system of equations to

fi nd the distance for which the costs are the same on a one-day

rental.

11. Suppose a school has 1,200 students and is growing at a rate of 100

students per year. The neighboring school has 1,000 students and is

growing at a rate of 150 students per year. After how many years will

the schools have the same number of students? How many students will

they each have?

12. At a Mexican take-out restaurant one family ordered 5 burritos and 4

tacos. The burritos and tacos cost $17.50, not including tax. Another

family ordered 9 burritos and 5 tacos. Their burritos and tacos cost

$27.65 before tax. What is the cost of 1 burrito at this restaurant? What

is the cost of 1 taco?

10-2B



446 Algebra

Name

Copyr

ight

© W

right

Gro

up/M

cG

raw

-Hill


Lesson Master

SKILLS Objective A

In 1–10, a system is given. Solve each system by substitution.

1. x = 2y - 4

3x - 5y = −11

2. g = 2h + 3

4g - 3h = −3

3. n = 4m - 10

2n - 3m = 0

4. y = 0.4z - 2.4

4y - 10z = −18

5. a + 7b = 49

b = 7 + a

6. 4y - 2x = 2

x = 2 __

3 y

7. 0.2c - 0.4d = −0.4

c = d - 2

8. 3x - y = −2

y = 2x + 12

9. x - y = 5

2x + y = 1

10. b = −2a + 2

a = b + 7

10-3B


Algebra 447

Name

Copyrig

ht ©

Wrig

ht G

roup/M

cG

raw

-Hill

page 210-3B

SKILLS Objective A

11. To help Kyle study for a test, Cary 2x - 6y = 8

8x - 2y = 10

2x - 6y = 8

x =

6y + 8 _____

2

asked him to solve the system

Kyle’s solution was (1, -1). Check his

solution by fi lling in the missing portions at x =

the right. Was Kyle’s solution correct? 8( ) - 2y = 10

- 2y = 10

22y + 32 = 10

22y =

y = and

x =

USES Objective G

12. Students having a brownie and cookie sale sold 38 items and earned a

total of $47.25. They sold brownies for $1.50 each and cookies for $0.75

each.

a. Let b = the number of brownies they sold and c = the number

of cookies they sold. Write a system of equations for this situation.

b. How many cookies did they sell? How many brownies did they sell?

13. A teacher is writing a test that is worth 100 points. Some of the

questions are worth 4 points each and the rest of the questions are

worth 5 points each. There is a total of 23 questions on the test.

a. Describe the situation with a system of equations.

b. How many of each kind of question is on the test?



Algebra 449

Name

Copyrig

ht ©

Wrig

ht G

roup/M

cG

raw

-Hill

Lesson Master

SKILLS Objective B

In 1–8, a system is given. Solve the system using addition.

1. 3x - 2y = −5

4x + 2y = −16

2. 3r - 5s = −7

−3r + 2s = 1

3. 2m - n = 4

1.2m - 0.3n = 1.5

4. x - y = − 1 __

5

10x + 5y = 7

5. 3a - 2b = −8

−3a + 4b = 16

6. 1

__ 2 m - n = −30

m + n = 15

7. 2a + b = −80

−3a + b = 120

8. 4x - 2y = 0

4x + y = 0

10-4B Questions on SPUR ObjectivesSee pages 650–653 for objectives.


450 Algebra

Name

Copyr

ight

© W

right

Gro

up/M

cG

raw

-Hill

page 2

9. The ordered pair (H, K) = (134, 256) is the solution to the system of

equations 5H + 6K = 2,206

-8H + 3K = −304

. Check the solution in both equations.

10. Is (x, y) = (−100, 3) a solution to the system of equations

4x - 2y = −406

3x + 5y = −315

? Explain.

USES Objective G

11. Two people paddle a canoe 8 miles upstream in two hours. Then they

turn around and paddle 8 miles downstream in one hour. If they are

paddling at the same rate both upstream and downstream, how fast are

they paddling? How fast is the current?

12. A family has adopted a total of 13 cats and dogs from the local animal

shelter. The number of cats they have is 2 less than twice the number of

dogs. How many cats and dogs do they have?

13. At a furniture store, you can purchase 2 fl oor lamps and 3 table lamps

for $360, or 3 fl oor lamps and 1 table lamp for $330. What is the cost of

one fl oor lamp? What is the cost of one table lamp?

14. On a lunch menu, a turkey sandwich with a cup of soup is $6.00 and a

half of a turkey sandwich with a cup of soup is $3.75. Assuming the half

sandwich costs exactly half as much as the whole sandwich, how much

does the cup of soup cost?

10-4B



452 Algebra

Name

Copyr

ight

© W

right

Gro

up/M

cG

raw

-Hill


Lesson Master

SKILLS Objective B

1. Consider the system 3x - 2y = −5

6x - 3y = −12

.

a. What operation was done to the system to

get −6x + 4y = 10

6x - 3y = −12

?

b. Solve the system.

2. Consider the system 2c + 8d = 68

4c - 2d = 28

.

a. If the second equation in the system is multiplied

by 4, then adding the equations will eliminate

what variable?


3. Consider the system 2x - y = −13

3x + 2y = −2

.

a. If the fi rst equation in the system is multiplied

by 2, then adding the equations will eliminate

what variable?


In 4–6, solve the system.

4. −3x + y = 8

x - 2y = −1

5. 4y - x = 8

y + 2x = 2

6. 2a - 5b = 31

8a + b = 19

10-5B


Algebra 453

Name

Copyrig

ht ©

Wrig

ht G

roup/M

cG

raw

-Hill

page 2

In 7–9, solve the system.

7. 1 _ 2 m + 3 _ 2 n = −5

7 _ 2 m - 5 _ 2 n = 43

8. 0.5x - 0.2y = 0

0.4x + 0.8y = 0

9. 4 _ 5 x + y = 1

2x - 10

__ 3 y = -1

USES Objective G

10. The difference of the smaller of two integers and twice the larger

integer is −7. The sum of −3 times the smaller integer and 5 times the

larger integer is 18. What are the two integers?

11. At an ice cream store, one family bought three medium ice cream cones

and two sundaes for $9. Another family bought fi ve medium cones and

one sundae for $9.75. What is the cost of a sundae and what is the cost

of a medium ice cream cone at the store?

12. At a dog park, an observer noticed that, counting all of the dogs and

people, there were 80 legs and 25 heads in the crowd. How many dogs

were at the park? How many people were at the park?

13. At a library book sale, paperback books cost $0.50 each and hardback

books cost $1.25 each. At the sale, they sold 80 books and made $62.50.

How many paperback books did they sell? How many hardback books

did they sell?

10-5B



Algebra 455

Name

Copyrig

ht ©

Wrig

ht G

roup/M

cG

raw

-Hill

Lesson Master

PROPERTIES Objective F

In 1–6, describe the graph of the given system as intersecting lines, parallel

lines, or coincident lines.

1. 2x - 3y = −18

y = 4x + 16

2. 2x + 3y = 4

−4x - 6y = 6

3. y = 5x

4x - 5y = 0

4. 2x + 6y = 12

y = − 1 __

3 x + 2

5. y

__ 2 = 5 __

2 x - 3

10x - 2y = 4 6.

3x - 4y = 7

y = 3 __ 4 x - 7 __

4

7. Find the value of k so the graphs of the equations in the system

4y - 2x = 12

2y = kx - 8

are parallel lines.

8. Find the value of k so the graphs of the equations in the system

4y + 3x = 1

12y = kx + 3

are coincident lines.

9. True or false. If a = −10, the system 4x - 5y = 6

8x + ay = 12

will have infi nitely

many solutions.

10. True or false. If a = 3, the system 2x + 2y = 3

4x + ay = 1

will have

no solution.

10-6B Questions on SPUR ObjectivesSee pages 650–653 for objectives.


456 Algebra

Name

Copyr

ight

© W

right

Gro

up/M

cG

raw

-Hill

page 2

USES Objective G

11. During a recent store sale, all shirts were priced at $15 each, and shoes

were priced at $15 per pair. Molly reported that they sold 19 items total,

and Gus reported that they sold $300 worth of merchandise. Can both

Molly and Gus be correct? Explain.

12. Penny buys 2 cans of soup and 4 bags of grapes at the grocery store for

$16. Then she fi nds out they are having a 10% off sale on those items

the next day. She returns the next day and buys 1 can of soup and 2

bags of grapes, and the clerk tells her that her total after the discount is

$8.10. Did the clerk calculate correctly?


In 13–15, match each system of equations to its corresponding graph

and state the number of solutions. Each system is graphed in the

standard window.

13. y - 3x = 0

3x -y = 3

14. x - y = 2

2x + y = 7

15. 2x + 3y = 6

y = − 2 __

3 x + 2

A B C

10-6B



464 Algebra

Name

Copyr

ight

© W

right

Gro

up/M

cG

raw

-Hill


Lesson Master

USES Objective H

1. You set a spending limit of $600 for birthday gifts for your family and

friends this year. You will buy presents for 6 family members and 4

friends. You decide you want to spend at most $10 more on family

members than on friends. You will also spend the same amount for each

family member and the same amount for each friend.

a Write a system of inequalities that b. Graph the inequalities to show how much

describes the amount that you can spend you can spend on a family gift and on gift

on a gift for a family member x and on a for a friend.

gift for a friend y.

c. What is the maximum amount you can spend

on a gift for a family member?

d. What is the maximum amount you can spend

on a gift for a friend if you spend the maximum

on a family gift?

2. In a mountain bike relay race, together Nikki and Daronelle rode less

than 18 miles. Nikki rode at a slower rate than Daronelle. Daronelle rode

for 3 hours and Nikki rode for 2 hours.

a. Write a system of inequalities that b. Graph all combinations of possible rates

describes the rate d in miles per hour that for Daronelle and Nikki during the

Daronelle rode and the rate n in miles per bike race.

hour that Nikki rode.

c. What is the maximum rate at which

Daronelle could have ridden?

d. How far did Daronelle ride if she rode at

her maximum rate?

10-9B

x

y

d

n


Algebra 465

Name

Copyrig

ht ©

Wrig

ht G

roup/M

cG

raw

-Hill

page 2

REPRESENTATIONS Objective J, K

In 3–8, graph the solution to the system.

3. y < 2x + 1

y ≥ −4

4. 3x + y < −1

3x - 4y > 12

5. x ≤ −2

x + y >1

6.

y < 4x

x ≤ 1

y ≤ −2 7.

−2x + 3y < 6

x ≤ 4

y > −x - 2 8.

y > 1 __ 2 x - 2

y < −2x + 1

In 9–11, describe the shaded region with a system of inequalities.

9. 10. 11.

10-9B

x

y

x

y

x

y

x

y

x

y

x

y

1-1-2-4-5-6-7-8

1

-2

-3

-4

-5

-6

-7

-8

2

3

4

5

6

7

8

2 3 4 5 6 7 8

x

y

1-1-2-3-4-5-6-7-8

1

-1

-2

-3

-4

-6

-7

-8

2

3

4

5

6

7

8

2 4 5 6 7 8

x

y

1-1-2-3-4-5-6-7-8

1

-1

-2

-3

-4

-5

-6

-7

-8

2

3

4

5

6

7

8

2 3 4 5 6 7 8

x

y



466 Algebra

Name

Copyr

ight

© W

right

Gro

up/M

cG

raw

-Hill


SKILLS Objective E

In 1 and 2, solve the system.

1. y = x 2 - 4

y = 3

2. y = x 2 - 5

y = 4x

3. True or false. (−3, 8) is a solution to the system y = x 2 - 1

y = 8

.

4. How many solutions does the system x 2 + y = 8

y = 2x

have?


In 5 and 6, solve the system by graphing.

5. y = 2x + 2

y = x 2 + 2

6. y = x 2 - 6x + 9

y = 2x - 7

7. Randy graphed the system y = x 2 + 8x + 16

y = −x 2 - 8x -8

in

the standard window as shown at the right. Use

the graph to approximate the solutions

to the system.

10-10A Lesson Master

x

y

x

y


Documents

10-1B Lesson Master - North Hunterdon-Voorhees Regional ... · Two people paddle a canoe 8 miles upstream in two hours. Then they turn around and paddle 8 miles downstream in one