1

ALGEBRA 1

Teacher:

Unit 3

Chapter 6

This book belongs to:

UPDATED FALL 2016

2

3

Algebra 1

Section 6.1 Notes: Graphing Systems of Equations

Day 1

Warm-Up

1. Graph 𝑦 = 3𝑥 − 1 on a coordinate plane. 2. Check to see if (2, 5) is a solution to the equation

𝑦 = 3𝑥 − 1.

____________________________________________________________________________________________________________

Example 1: Use the graph to the right to solve the system. Then, check your solution algebraically.

??How many solutions are there to the system of linear equations above?? ________________

Is there always this many solutions?

Possible Solutions Summary

A system of equations, or a linear system, consists of two or more ________________ equations in the same

variables.

A solution of a system of linear equations in two variables is where ______________ _______________________.

Solve each system of equations by graphing and finding the point of intersection. Solutions found by graphing

should be ________________ algebraically.

4

Example 2: Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely

many solutions. If the system has one solution, name it.

a) y = 2x + 3

8x – 4y = –12

b) x – 2y = 4 c) x – y = 2

x – 2y = –2 3y + 2x = 9

Example 3: Line k is represented by the equation 𝑦 =1

2𝑥 − 5 and Line z is graphed below. At which point would Line k and

Line z intersect?

Solving a Linear System by Graphing Step 1: Start by _______________ each of the

equations. Hint: It might help to write

each equation in ____________

________________ form first.

Step 2: Estimate the coordinates of the point

of intersection (________________).

Step 3: ____________ the coordinates

algebraically by substituting into BOTH

equations of the original linear system.

5

Example 4: Which graph displays the solution to the system: 2𝑥 + 𝑦 = −2

𝑥 + 𝑦 = 2

A) B)

C) D)

Example 5: Which graph displays the solution to the system: 5𝑥 + 5𝑦 = 15

3𝑥 + 6𝑦 = 3

A) B)

C) D)

6

7

Algebra 1

Section 6.1 Notes: Graphing Systems of Equations

Day 2

Warm-Up

1. Graph the system and find the solution.

𝑦 = −2𝑥 + 5

𝑦 =1

3𝑥 − 2

____________________________________________________________________________________________________________

Example 6: Naresh and Diego are having a bicycling competition. Naresh is able to ride 20 miles at the start of the

competition and plans to ride 35 more miles than the previous week each upcoming week. Diego is able to ride 50 miles at

the start of the competition and plans to ride 25 more miles than the previous week each upcoming week. Predict the week

in which Naresh and Diego will have ridden the same number of miles.

Story Time: Math Libs!! ___________________ is running a business that rents in-line skates, for $15 a day, and ____________________, for $30 a

day. During one day, ______________________’s business has a total of 25 rentals and collects $450 for the rentals. Find

the number of pairs of skates rented and the number of ______________________ rented.

a) Write a linear system. Let x be the number of skates and y be the number of _____________________ rented.

b) Graph both equations.

c) Estimate the point of intersection.

d) Check whether ( , ) is a solution.

(noun) (Name)

(Name)

(noun)

(noun)

8

Example 7: A delivery service offers two package sizes. x represents the cost of a large package and y represents the cost of

a small package. On Monday, the service delivered 40 large and 20 small packages for a cost of $380. On Tuesday, 32

large and 80 small packages were delivered for $496. Based on the graph for Monday and Tuesday, which is closest to the

cost to deliver each type of package?

A) Large $3, Small $8

B) Large $8, Small $3

C) Large $6, Small $9

D) Large $9, Small $6

Example 8: Rayna paid a $200 fee to join a health club and then a $50 fee per month to use the club. Nora Paid a $100

fee to join a different health club and then a $75 fee per month to use the club. The equations and graph below can be

used to determine how many months (m) and the total cost (t) for the girls at the health clubs.

Rayna: 𝑡 = 50𝑚 + 200

Nora: 𝑡 = 75𝑚 + 100

a. In what month will the girls have paid an equal

amount for their health club fees?

b. What is their total fee for that month?

c. For which months is Rayna’s total cost for the

health club less than Nora’s total cost?

9

Algebra 1

Section 6.1 Worksheet

Use the graph at the right to determine whether

each system is consistent or inconsistent and

if it is independent or dependent.

1. x + y = 3 2. 2x – y = –3

x + y = –3 4x – 2y = –6

3. x + 3y = 3 4. x + 3y = 3

x + y = –3 2x – y = –3

Graph each system and determine the number of solutions that it has. If it has one solution, name it.

5. 3x – y = –2 6. y = 2x – 3 7. x + 2y = 3

3x – y = 0 4x = 2y + 6 3x – y = –5

8. BUSINESS Nick plans to start a home-based business

producing and selling gourmet dog treats. He figures it

will cost $20 in operating costs per week plus $0.50 to

produce each treat. He plans to sell each treat for $1.50.

a. Graph the system of equations y = 0.5x + 20 and

y = 1.5x to represent the situation.

b. How many treats does Nick need to sell per week to break even?

9. SALES A used book store also started selling used

CDs and videos. In the first week, the store sold 40

used CDs and videos, at $4.00 per CD and $6.00 per

video. The sales for both CDs and videos totaled $180.00

a. Write a system of equations to represent the situation.

b. Graph the system of equations.

c. How many CDs and videos did the store sell in the first week?

10

11

Algebra 1

Section 6.2 Notes: Substitution

Day 1

Warm-Up

Graph the system of equations. Then determine whether the system has no solution,

one solution, or infinitely many solutions. If the system has one solution, name it.

3𝑥 = 11 − 𝑦 A. one; (4, –1)

𝑥 − 2𝑦 = 6

B. one; (2, 2)

C. infinitely many solutions

D. no solution

____________________________________________________________________________________________________________

Example 1: Use substitution to solve the system of equations.

a) y = –4x + 12 b) y = 4x – 6

2x + y = 2 5x + 3y = -1

Steps for Solving by Substitution

1) When necessary, solve for ________________________________.

2) __________________ the resulting expression from Step 1 into the other equation.

3) __________________ the equation.

4) __________________ this variable in to solve for the other _________________.

5) ______________ your answer.

12

Example 2: Use substitution to solve the system of equations.

a) x – 2y = –3 b) 3x – y = –12

3x + 5y = 24 –4x + 2y = 20

How do you know which variable to solve for?

Example 3: The substitution method will be used to solve the system. Which equation below would be a step in this

process? x + 2y = 15

5x + y = 21

A) 5(2𝑦 + 15) + 𝑦 = 21 B) 5(15 – 2𝑦) = 21

C) 5(15 – 2𝑦) + 𝑦 = 21 D) 15 − 2𝑦 + 𝑦 = 21

13

Algebra 1

Section 6.2 Notes: Substitution

Day 2

Warm-Up

1. Solve using substitution. 𝑦 = 2𝑥 + 1

𝑥 + 4𝑦 = 22

2. Today Tom has $100 in his savings account, and plans to put $25 in the account every week. Maria has nothing in her

account, but plans to put $50 in her account every week. In how many weeks will they have the same amount in their

accounts? How much will each person have saved at that time?

A. 6 weeks; $300

B. 5 weeks; $250

C. 4 weeks; $200

D. 3 weeks; $150

____________________________________________________________________________________________________________

Example 4: Use substitution to solve the system of equations.

a) 2x + 2y = 8 b) 3x – 2y = 3

x + y = –2 –6x + 4y = –6

14

Example 5:

a) A nature center charges $35.25 for a yearly membership and $6.25 for a single admission. Last week it sold a

combined total of 50 yearly memberships and single admissions for $660.50. How many memberships and

how many single admissions were sold?

b) As of 2009, the New York Yankees and the Cincinnati Reds together had won a total of 32 World Series. The

Yankees had won 5.4 times as many as the Reds. How many World Series had each team won?

Example 6: What is the value of y in this system of equations?

5𝑥 − 8 = 𝑦

4𝑥 + 3𝑦 = 33

15

Algebra 1

6.2 Worksheet

Use substitution to solve each system of equations.

1. y = 6x 2. x = 3y 3. x = 2y + 7

2x + 3y = –20 3x – 5y = 12 x = y + 4

4. y = 2x – 2 5. y = 2x + 6 6. 3x + y = 12

y = x + 2 2x – y = 2 y = –x – 2

7. x + 2y = 13 8. x – 2y = 3 9. x – 5y = 36

–2x – 3y = –18 4x – 8y = 12 2x + y = –16

10. 2x – 3y = –24 11. x + 14y = 84 12. 0.3x – 0.2y = 0.5

x + 6y = 18 2x – 7y = –7 x – 2y = –5

13. 0.5x + 4y = –1 14. 3x – 2y = 11 15. 1

2𝑥 + 2y = 12

x + 2.5y = 3.5 x – 1

2𝑦 = 4 x – 2y = 6

16. 1 – 3 x – y = 3 17. 4x – 5y = –7 18. x + 3y = –4

2x + y = 25 y = 5x 2x + 6y = 5

16

19. EMPLOYMENT Kenisha sells athletic shoes part-time at a department store. She can earn either $500 per month plus a 4%

commission on her total sales, or $400 per month plus a 5% commission on total sales.

a. Write a system of equations to represent the situation.

b. What is the total price of the athletic shoes Kenisha needs to sell to earn the same income from each pay scale?

c. Which is the better offer?

20. MOVIE TICKETS Tickets to a movie cost $7.25 for adults and $5.50 for students. A group of friends purchased

8 tickets for $52.75.

a. Write a system of equations to represent the situation.

b. How many adult tickets and student tickets were purchased?

21. BUSINESS Mr. Randolph finds that the supply and demand for gasoline at his station are generally given by the following

equations.

x – y = –2

x + y = 10

Use substitution to find the equilibrium point where the supply and demand lines intersect.

22. GEOMETRY The measures of complementary angles have a sum of 90 degrees. Angle A and angle B are complementary, and

their measures have a difference of 20°. What are the measures of the angles?

23. MONEY Harvey has some $1 bills and some $5 bills. In all, he has 6 bills worth $22. Let x be the number of $1 bills and let y be

the number of $5 bills. Write a

system of equations to represent the information and use substitution to determine how many bills of each

denomination Harvey has.

24. POPULATION Sanjay is researching population trends in South America. He found that the population of Ecuador to increased

by 1,000,000 and the population of Chile to increased by 600,000 from 2004 to 2009. The table displays the information he found.

Country 2004

Population

5-Year Population

Change

Ecuador 13,000,000 +1,000,000

Chile 16,000,000 +600,000

Source: World Almanac

If the population growth for each country continues at the same rate, in what year are the populations of Ecuador and Chile

predicted to be equal?

17

Algebra 1 6.1 – 6.2 Quiz Review Name:

1. Use the graph to determine how many solutions the system below has.

𝑥 + 𝑦 = −2

𝑦 =1

3𝑥 +

2

3

2. Solve the system by graphing. 3. If 𝑥 + 𝑦 = 3 and 𝑥 − 𝑦 = 3, find the value of x.

−2𝑥 + 𝑦 = 5

3𝑥 + 2𝑦 = −4

4. Solve by substitution.

2𝑦 − 𝑥 = −8

3𝑥 + 𝑦 = −4

5. You are helping a school fundraiser by selling baked goods. You sell a muffin for $1.50 and cookies for $1. At the

end of the fundraiser you sold 113 baked goods (muffins and cookies combined) and make a total of $133.50. Write a

system of equations and solve using substitution. Find the number of muffins sold and the number of cookies sold.

a. No Solution

b. One Solution

c. Infinitely Many solutions

d. Cannot be determined

18

19

Algebra 1

Section 6.3 Notes: Elimination Using Addition and Subtraction

Warm-Up

1. Find the opposite of each term. 2. Add the two equations together to obtain a new

equation.

a. 4x b. –y −2𝑥 + 3𝑦 = 4

4𝑥 − 3𝑦 = −6

Now solve for x.

____________________________________________________________________________________________________________

Example 1: Use elimination to solve the system of equations.

a) –3x + 4y = 12 b) 3x – 5y = 1

3x – 6y = 18 2x + 5y = 9

Example 2: Four times one number minus three times another number is 12. Two times the first number added to three

times the second number is 6. Write a system of linear equations and then use elimination to solve it and find the numbers.

Steps for Solving by Elimination with Addition/Subtraction

1) Arrange the equations in ______________________ form.

2) _____________ or _______________ the equations to eliminate one variable and solve.

3) Substitute the value from Step 2 into one of the equations and ___________________.

4) Check your answer!!

20

Example 3: Use elimination to solve the system of equations.

a) 4x – 28 = –2y b) 9x – 2y = 30

4x – 3y = 18 – 2y + x = 14

Example 4:

a) A hardware store earned $956.50 from renting ladders and power tools last week. The store charged 36 days

for ladders and 85 days for power tools. This week the store charged 36 days for ladders, 70 days for power

tools, and earned $829. How much does the store charge per day for ladders and for power tools?

b) For a school fundraiser, Marcus and Anisa participated in a walk-a-thon. In the morning, Marcus walked 11

miles and Anisa walked 13. Together they raised $523.50. After lunch, Marcus walked 14 miles and Anisa

walked 13. In the afternoon they raised $586.50. How much did each raise per mile of the walk-a-thon?

21

Algebra 1

6.3 Worksheet

Use elimination to solve each system of equations.

1. x – y = 1 2. p + q = –2 3. 4x + y = 23

x + y = –9 p – q = 8 3x – y = 12

4. 2x + 5y = –3 5. 3x + 2y = –1 6. 5x + 3y = 22

2x + 2y = 6 4x + 2y = –6 5x – 2y = 2

7. 5x + 2y = 7 8. 3x – 9y = –12 9. –4c – 2d = –2

–2x + 2y = –14 3x – 15y = –6 2c – 2d = –14

10. 2x – 6y = 6 11. 7x + 2y = 2 12. 4.25x – 1.28y = –9.2

2x + 3y = 24 7x – 2y = –30 x + 1.28y = 17.6

13. 2x + 4y = 10 14. 2.5x + y = 10.7 15. 6m – 8n = 3

x – 4y = –2.5 2.5x + 2y = 12.9 2m – 8n = –3

16. 4a + b = 2 17. – 1

3x –

4

3 = –2 18.

3

4x –

1

2𝑦 = 8

4a + 3b = 10 1

3 x –

2

3𝑦 = 4

3

2 x –

1

2𝑦 = 19

22

19. The sum of two numbers is 41 and their difference is 5. What are the numbers?

20. Four times one number added to another number is 36. Three times the first number minus the other number is 20. Find the

numbers.

21. One number added to three times another number is 24. Five times the first number added to three times the other number is 36.

Find the numbers.

22. LANGUAGES English is spoken as the first or primary language in 78 more countries than Farsi is spoken as the first

language. Together, English and Farsi are spoken as a first language in 130 countries. In how many countries is English spoken

as the first language? In how many countries is Farsi spoken as the first language?

23. DISCOUNTS At a sale on winter clothing, Cody bought two pairs of gloves and four hats for $43.00. Tori bought two pairs of

gloves and two hats for $30.00. What were the prices for the gloves and hats?

23

Algebra 1

Section 6.4 Notes: Elimination Using Multiplication

Warm-Up

1. Use elimination to solve the system of equations. 5𝑥 + 𝑦 = 9

3𝑥 − 𝑦 = 7

A. (2, –1)

B. (–2, 1)

C. (4, –3)

D. (5, –2)

2. Use elimination to solve the system of equations. 2𝑥 + 4𝑦 = −8

2𝑥 − 1 = −𝑦

A. (3, –2)

B. (2, –3)

C. (1, 3)

D. (–1, 2)

3. Find two numbers that have a sum of 151 and a difference of 7.

A. 67, 84

B. 69, 82

C. 71, 80

D. 72, 79

___________________________________________________________________________________________________________

Example 1: Use elimination to solve the system of equations.

a) 2x + y = 23 b) x = 12 – 7y

3x + 2y = 37 3x – 5y = 10

Steps for Solving by Elimination with Multiplication

1) Arrange the equations in ______________________ form.

2) _________________________ at least one equation by a constant to get the coefficients of

one variable to contain opposite terms.

3) _____________ or _______________ the equations to eliminate one variable and solve.

4) Substitute the value from Step 3 into one of the equations and ___________________.

5) Check your answer!!

24

Example 2: Use elimination to solve the system of equations.

a) 4x + 3y = 8 b) 3x + 2y = 10

– 5y = –23 – 3x 2x + 5y = 3

Example 3:

a) Nathan is thinking of two numbers. Adding 10 times the first number and 3 times the second number gives a

total of 26. Also, adding 10 times the first number and 8 times the second number gives 36. What are the two

numbers?

b) Dalton has 7 bills, all tens and twenties, that total $100 in value. How many of each bill does he have?

Example 4: Which operations on the system of equation will solve for the y quantity? 8x – 7y = 5

3x – 5y = 9

A) Multiply the first equation by 3 and the second equation by 8 and add the resulting equations

B) Multiply the first equation by – 5 and the second equation by 7 and add the resulting equations

C) Multiply the first equation by – 3 and the second equation by – 8 and add the resulting equations

D) Multiply the first equation by – 3 and the second equation by 8 and add the resulting equations

25

Algebra 1

6.4 Worksheet

Use elimination to solve each system of equations.

1. 2x – y = –1 2. 5x – 2y = –10 3. 7x + 4y = –4

3x – 2y = 1 3x + 6y = 66 5x + 8y = 28

4. 2x – 4y = –22 5. 3x + 2y = –9 6. 4x – 2y = 32

3x + 3y = 30 5x – 3y = 4 –3x – 5y = –11

7. 3x + 4y = 27 8. 0.5x + 0.5y = –2 9. 2x – 3

4𝑦 = –7

5x – 3y = 16 x – 0.25y = 6 x + 1

2𝑦 = 0

10. 6x – 3y = 21 11. 3x + 2y = 11 12. –3x + 2y = –15

2x + 2y = 22 2x + 6y = –2 2x – 4y = 26

26

13. Eight times a number plus five times another number is –13. The sum of the two numbers is 1. What are the numbers?

14. Two times a number plus three times another number equals 4. Three times the first number plus four times the other number is 7.

Find the numbers.

15. FINANCE Gunther invested $10,000 in two mutual funds. One of the funds rose 6% in one year, and the other rose 9% in one

year. If Gunther’s investment rose a total of $684 in one year, how much did he invest in each mutual fund?

16. CANOEING Laura and Brent paddled a canoe 6 miles upstream in four hours. The return trip took three hours. Find the rate at

which Laura and Brent paddled the canoe in still water.

17. NUMBER THEORY The sum of the digits of a two-digit number is 11. If the digits are reversed, the new number is 45 more

than the original number. Find the number.

27

Algebra 1 6.3 – 6.4 Quiz Review

For Numbers 1 – 3 solve the systems of equations using elimination:

1. 4𝑥 + 5𝑦 = 8 2. 7𝑥 + 9𝑦 = 6 3. 5𝑥 + 2𝑦 = −18

−4𝑥 − 3𝑦 = 0 5𝑥 + 3𝑦 = 18 −3𝑥 + 7𝑦 = 19

4. Find the value of x in the following system 5. Determine whether (–4, 5) is a solution to the

of equations: following system of equations:

4𝑥 − 𝑦 = 6 𝑥 + 3𝑦 = 11

8𝑥 + 𝑦 = 6 5𝑥 + 6𝑦 = 1

6. In the first hour of sales, an aquarium sold 20 tickets for $168. Children tickets cost $6 and adult tickets cost $9.

a. Define your variables.

b. Write a system of equations to represent the situation.

c. Solve the system of equations using elimination.

d. How many adult tickets were sold? How many children tickets were sold?

28

29

Algebra 1

Section 6.5 Notes: Applying Systems of Linear Equations

Warm-Up

1. Use elimination to solve the system of equations. 2𝑎 + 𝑏 = 19

3𝑎 − 2𝑏 = −3

A. (9, 5)

B. (6, 5)

C. (5, 9)

D. No solution

2. Use elimination to solve the system of equations. 8𝑥 + 12𝑦 = 1

2𝑥 + 3𝑦 = 6

A. (3, 1)

B. (3, 2)

C. (3, 4)

D. No solution

____________________________________________________________________________________________________________

Quick Practice: Look at the following examples below and decide which method is the best to use to solve the system of

equations. Don’t actually solve them (unless you want the extra practice). Your 5 choices are graphing, substitution,

elimination using addition, elimination using subtraction, and elimination using multiplication.

a) b) c) d)

Best Method to Use

Method Best Time to Use it

Graphing

Substitution

Elimination Using Addition

Elimination Using Subtraction

Elimination Using Multiplication

30

Example 1: Determine the best method to solve the system of equations. Then solve the system.

a) POOL PARTY At the school pool party, Mr. Lewis bought 1 adult ticket and 2 child tickets for $10.

Mrs. Vroom bought 2 adult tickets and 3 child tickets for $17. How much do adult and child tickets cost?

b) CAR RENTAL Ace Car Rental rents a car for $45 and $0.25 per mile. Star Car Rental rents a car for $35 and

$0.30 per mile. How many miles would a driver need to drive before the cost of renting a car at Ace Car Rental

and renting a car at Star Car Rental were the same?

c) VIDEO GAMES The cost to rent a video game from Action Video is $2 plus $0.50 per day. The cost to rent a

video game at TeeVee Rentals is $1 plus $0.75 per day. After how many days will the cost of renting a video game

at Action Video be the same as the cost of renting a video game at TeeVee Rentals?

31

Algebra 1

6.5 Worksheet

Warm-Up

1. Two hiking groups made the purchases shown in the chart. What is the cost of each item?

A. muffin, $1.60;

granola bar, $1.25

B. muffin, $1.25; granola bar, $1.60

C. muffin, $1.30; granola bar, $1.50

D. muffin, $1.50; granola bar, $1.30

Determine the best method to solve each system of equations. Then solve the system.

1. 5x + 3y = 16 2. 3x – 5y = 7

3x – 5y = –4 2x + 5y = 13

3. y = 3x – 24 4. –11x – 10y = 17

5x – y = 8 5x – 7y = 50

5. 4x + y = 24 6. 6x – y = –145

5x – y = 12 x = 4 – 2y

32

7. VEGETABLE STAND A roadside vegetable stand sells pumpkins for $5 each and squashes for $3 each. One day they sold 6 more

squash than pumpkins, and their sales totaled $98. Write and solve a system of equations to find how many pumpkins and quash

they sold?

8. INCOME Ramiro earns $20 per hour during the week and $30 per hour for overtime on the weekends. One week Ramiro earned a

total of $650. He worked 5 times as many hours during the week as he did on the weekend. Write

and solve a system of equations to determine how many hours of overtime Ramiro worked on the weekend.

9. BASKETBALL Anya makes 14 baskets during her game. Some of these baskets were worth 2-points and others were worth 3-

points. In total, she scored 30 points. Write and solve a system of equations to find how 2-points baskets she made.

33

x

y

x

y

Algebra 1

Section 6.6 Notes: Systems of Inequalities

Warm-Up

Graph the following inequalities. Put in slope-intercept form, if necessary (y=mx+b).

1.) 𝑦 > 2𝑥 + 3 2.) 4𝑥 − 3𝑦 ≥ 6

m = m =

b = b =

If > or ≥, shade ____________________

If < or ≤, shade ____________________

*Note: Inequality must be in slope-intercept form

___________________________________________________________________________________________________________

Example 1: Solve the system of inequalities by graphing.

a) y < 2x + 2

y ≥ – x – 3

What is your solution? How many solutions do you have?

b) y + 2 ≥ –3(x – 1)

–2y ≥ 6x + 4

34

Example 2: Choose the correct solution to the system: 2x + y ≥ 4 and x + 2y > –4.

Example 3:

Story Time!!

_____________ is buying wings and ______________ for a party. One

(name) (noun)

package of wings costs $1 and one package of ____________ costs $2.

(noun)

______________ cannot spend more than $10. ____________ also knows

(name) (name)

he will buy at most a total of 6 items.

a) Write a system of linear inequalities to represent this situation and

graph the system.

b) Find at least 2 solutions.

A. B.

C. D.

35

Example 4: A furniture store is offering discounts of 30% on a blue couch and 60% on a white couch. The original cost of

the couch is more than $1260. The total discounted cost of the couches is more than $630. If b represents the original cost

of the blue couch and w represents the original cost of the white couch, which system of inequalities can be used to find the

possible values of b and w?

A) 𝑏 + 𝑤 > 1260 B) 𝑏 + 𝑤 > 1260 C) 𝑏 + 𝑤 > 1260 D) 𝑏 + 𝑤 > 1260

0.3𝑏 + 0.6𝑤 > 630 0.6𝑏 + 0.3𝑤 > 630 0.7𝑏 + 0.4𝑤 > 630 0.4𝑏 + 0.7𝑤 > 630

Example 5: Eugenia needs to buy hamburgers and hot dogs for a picnic. She only has $28 to spend and must buy at least

80 hamburgers or hotdogs. A store charges $0.50 per hamburger and $0.25 per hot dog. The following inequalities,

where x represents the number of hamburgers bought and y represents the number of hot dogs bought, can be used to

represent this situation.

0.50𝑥 + 0.25𝑦 ≤ 28

𝑥 + 𝑦 ≥ 80

Which could be a possibility for the number of hamburgers and hot dogs bought?

A) 30 hamburgers, 51 hot dogs

B) 32 hamburgers, 49 hot dogs

C) 35 hamburgers and 44 hot dogs

D) 52 hamburgers and 28 hot dogs

36

37

6.6 Practice Worksheet

1. Which graph represents the solution of 𝑦 + 𝑥 < 0

𝑦 − 𝑥 > 0

A) B)

C) D)

2. Which graph represents the solution to the system of linear inequalities? 3𝑥 − 7𝑦 > 14

5𝑥 + 2𝑦 < −10

A) B) C) D)

3. Which graph represents the solution to the system of linear inequalities? 𝑦 ≤ 2𝑥 + 7

𝑦 ≤ −𝑥 − 2

A) B) C) D)

38

4. Which graph represents the solution to the system of linear inequalities? 𝑥 > −2

𝑦 ≤ 5

A) B) C) D)

5. Which graph represents the solution to the system of linear inequalities? 𝑦 ≤ 2𝑥 + 5

𝑦 ≥ 2𝑥 − 3

A) B) C) D)

6. What system of inequalities is represented in the graph?

A) y ≥ – 2x B) y ≥ – 2x

y < – 1

3x –

3

4 y > –

1

3x –

3

4

C) y ≤ – 2x D) y ≤ – 2x

y < – 1

3x –

3

4 y > –

1

3x –

3

4

7. What system of inequalities is represented in the graph?

A) y < –2x + 1

2 B) y < –2x +

1

2

y ≤ 1

5x –

1

2 y ≥

1

5x –

1

2

C) y > –2x + 1

2 D) y > –2x +

1

2

y ≤ 1

5x –

1

2 y ≥

1

5x –

1

2

39

Algebra 1

6.6 Worksheet

Warm-Up

1. Solve the system of equations. 5𝑥 − 2𝑦 = 18

𝑥 + 2𝑦 = −6

A. (2, –4)

B. (2, –3)

C. (1, 3)

D. (0, 9)

Solve each system of inequalities by graphing.

1. y > x – 2 2. y ≥ x + 2 3. x + y ≥ 1

y ≤ x y > 2x + 3 x + 2y > 1

4. y < 2x – 1 5. y > x – 4 6. 2x – y ≥ 2

y > 2 – x 2x + y ≤ 2 x – 2y ≥ 2

7. FITNESS Diego started an exercise program in which each week he works out at the

gym between 4.5 and 6 hours and walks between 9 and 12 miles.

a. Make a graph to show the number of hours Diego works out at the gym and the

number of miles he walks per week.

b. List three possible combinations of working out and walking that meet Diego’s goals.

8. SOUVENIRS Emily wants to buy turquoise stones on her trip to New Mexico to give to

at least 4 of her friends. The gift shop sells stones for either $4 or $6 per stone. Emily

has no more than $30 to spend.

a. Make a graph showing the numbers of each price of stone Emily can purchase.

b. List three possible solutions.

40

41

Algebra 1 6.5 – 6.6 Review

For numbers 1 – 3, determine the best method to solve each system of equations. Then solve the system.

1. 2𝑥 − 3𝑦 = −7 2. 2𝑥 + 𝑦 = 0 3. 𝑥 = −𝑦

𝑦 = −3𝑥 − 5 𝑥 + 𝑦 = 5 3𝑥 + 2𝑦 = 1

4. You are selling lollipops and Cake Pops for your school fundraiser. Lollipops cost $1.00 each and Cake

Pops cost $1.50. By the end of the week, you sold 36 total pops (both lollipops and cake pops) and you made

$44.50. How many of each type of pop did you sell?

5. a. Solve the system of inequalities by graphing. {𝑦 < −

1

2𝑥 + 2

𝑦 ≤3

4𝑥 + 2

b. Give an ordered pair that is a solution: