ALGEBRA 1. Unit 3 Chapter 6. This book belongs to: Teacher:

Size: px
Start display at page:

Download "ALGEBRA 1. Unit 3 Chapter 6. This book belongs to: Teacher:"

Transcription

1 ALGEBRA 1 Teacher: Unit 3 Chapter 6 This book belongs to: UPDATED FALL

2 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. 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. 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 3

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 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. 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 x 5 and Line z is graphed below. At which point would Line k and 2 Line z intersect? 4

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) 5

6 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 3 x 2 Story Time: Math Libs!! is running a business that rents in-line skates, for $15 a day, and, for $30 a (Name) (noun) day. During one day, s business has a total of 25 rentals and collects $450 for the rentals. Find (Name) the number of pairs of skates rented and the number of rented. (noun) a) Write a linear system. Let x be the number of skates and y be the number of rented. (noun) b) Graph both equations. c) Estimate the point of intersection. d) Check whether (, ) is a solution. 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. 7

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 Nora: t = 75m 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? 8

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 = x 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 $ 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? 9

10 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 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. Example 1: Use substitution to solve the system of equations. a) y = 4x + 12 b) y = 4x 6 2x + y = 2 5x + 3y = -1 11

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 12

13 Algebra 1 Section 6.2 Notes: Substitution Day 2 Warm-Up 1. Solve using substitution. y = 2x + 1 x + 4y = 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 13

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 $ 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 14

15 Algebra 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 y = 2x 2 5. y = 2x x + y = 12 y = x + 2 2x y = 2 y = x 2 7. x + 2y = x 2y = 3 9. x 5y = 36 2x 3y = 18 4x 8y = 12 2x + y = x 3y = x + 14y = x 0.2y = 0.5 x + 6y = 18 2x 7y = 7 x 2y = x + 4y = x 2y = x + 2y = 12 2 x + 2.5y = 3.5 x 1 y = 4 x 2y = x y = x 5y = x + 3y = 4 2x + y = 25 y = 5x 2x + 6y = 5 15

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 $ 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 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 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? 16

17 Algebra Quiz Review Name: 1. Use the graph to determine how many solutions the system below has. x + y = 2 y = 1 3 x a. No Solution b. One Solution c. Infinitely Many solutions d. Cannot be determined 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 $ Write a system of equations and solve using substitution. Find the number of muffins sold and the number of cookies sold. 17

18 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. 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!! 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. 19

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 $ 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 $ After lunch, Marcus walked 14 miles and Anisa walked 13. In the afternoon they raised $ How much did each raise per mile of the walk-a-thon? 20

21 Algebra Worksheet Use elimination to solve each system of equations. 1. x y = 1 2. p + q = x + y = 23 x + y = 9 p q = 8 3x y = x + 5y = x + 2y = x + 3y = 22 2x + 2y = 6 4x + 2y = 6 5x 2y = x + 2y = x 9y = c 2d = 2 2x + 2y = 14 3x 15y = 6 2c 2d = x 6y = x + 2y = x 1.28y = 9.2 2x + 3y = 24 7x 2y = 30 x y = x + 4y = x + y = m 8n = 3 x 4y = x + 2y = m 8n = a + b = x 4 3 = x 1 2 y = 8 4a + 3b = 10 1 x 2 y = 4 3 x 1 y =

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 $ Tori bought two pairs of gloves and two hats for $ What were the prices for the gloves and hats? 22

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 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!! Example 1: Use elimination to solve the system of equations. a) 2x + y = 23 b) x = 12 7y 3x + 2y = 37 3x 5y = 10 23

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 24

25 Algebra Worksheet Use elimination to solve each system of equations. 1. 2x y = x 2y = x + 4y = 4 3x 2y = 1 3x + 6y = 66 5x + 8y = x 4y = x + 2y = x 2y = 32 3x + 3y = 30 5x 3y = 4 3x 5y = x + 4y = x + 0.5y = x 3 y = 7 4 5x 3y = 16 x 0.25y = 6 x y = x 3y = x + 2y = x + 2y = 15 2x + 2y = 22 2x + 6y = 2 2x 4y = 26 25

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. 26

27 Algebra Quiz Review For Numbers 1 3 solve the systems of equations using elimination: 1. 4x + 5y = x + 9y = x + 2y = 18 4x 3y = 0 5x + 3y = 18 3x + 7y = 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? 27

28 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) Method Best Method to Use Best Time to Use it Graphing Substitution Elimination Using Addition Elimination Using Subtraction Elimination Using Multiplication 29

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? 30

31 Algebra 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 = x 5y = 7 3x 5y = 4 2x + 5y = y = 3x x 10y = 17 5x y = 8 5x 7y = x + y = x y = 145 5x y = 12 x = 4 2y 31

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. 32

33 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 ) 4x 3y 6 y y x m = m = b = b = x 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

34 Example 2: Choose the correct solution to the system: 2x + y 4 and x + 2y > 4. A. B. C. D. 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. 34

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 > b + 0.6w > b + 0.3w > b + 0.4w > b + 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 y 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 35

36 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) 37

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 x y > 1 x C) y 2x D) y 2x y < 1 x y > 1 x What system of inequalities is represented in the graph? A) y < 2x y 1 5 x 1 2 B) y < 2x y 1 5 x 1 2 C) y > 2x y 1 5 x 1 2 D) y > 2x y 1 5 x

39 Algebra Worksheet Warm-Up 1. Solve the system of equations. 5x 2y = 18 A. (2, 4) B. (2, 3) C. (1, 3) D. (0, 9) x + 2y = 6 Solve each system of inequalities by graphing. 1. y > x 2 2. y x x + y 1 y x y > 2x + 3 x + 2y > 1 4. y < 2x 1 5. y > x x 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. 39

40 40

41 Algebra Review For numbers 1 3, determine the best method to solve each system of equations. Then solve the system. 1. 2x 3y = x + 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 $ How many of each type of pop did you sell? 5. a. Solve the system of inequalities by graphing. { y < 1 2 x + 2 y 3 4 x + 2 b. Give an ordered pair that is a solution: 41

ALGEBRA 1 UNIT 3 WORKBOOK CHAPTER 6

ALGEBRA 1 UNIT 3 WORKBOOK CHAPTER 6 ALGEBRA 1 UNIT 3 WORKBOOK CHAPTER 6 FALL 2014 0 1 Algebra 1 Section 6.1 Notes: Graphing Systems of Equations System of Equations: a set of two or more equations with the same variables, graphed in the

More information

Study Guide and Intervention

Study Guide and Intervention 7-3 Study Guide and Intervention Elimination Using Addition and Subtraction Elimination Using Addition In systems of equations in which the coefficients of the x or y terms are additive inverses, solve

More information

Chapter 6: Systems of Linear Equations and Inequalities

Chapter 6: Systems of Linear Equations and Inequalities Lesson 6-1: Graphing Sstems of Equations Date: Eample 1: Use the graph to determine whether each sstem is consistent or inconsistent and if it is independent or dependent. a. = 1 and = + 1 b. = 1 and =

More information

You solved systems of equations by using substitution.

You solved systems of equations by using substitution. You solved systems of equations by using substitution. LEQ: How do we solve systems of equations by using elimination with addition & solve systems of equations by using elimination with subtraction? elimination

More information

Algebra I Practice Exam

Algebra I Practice Exam Algebra I This practice assessment represents selected TEKS student expectations for each reporting category. These questions do not represent all the student expectations eligible for assessment. Copyright

More information

Chapter 4: Systems of Equations and Inequalities

Chapter 4: Systems of Equations and Inequalities Chapter 4: Systems of Equations and Inequalities 4.1 Systems of Equations A system of two linear equations in two variables x and y consist of two equations of the following form: Equation 1: ax + by =

More information

Unit Test Linear equations and Inequalities

Unit Test Linear equations and Inequalities Unit Test Linear equations and Inequalities Name: Date: Directions: Select the best answer for the following questions. (2 points each) 7L 1. The steps for solving are: 1) Read the problem and label variables,

More information

Algebra I Chapter 6 Practice Test

Algebra I Chapter 6 Practice Test Name: Class: Date: ID: A Algebra I Chapter 6 Practice Test Multiple Choice Identify the choice that best completes the statement or answers the question. Find a solution of the system of linear inequalities.

More information

Name Algebra 1 Midterm Review Period. = 10 4x e) x ) Solve for y: a) 6x 3y = 12 b) 4y 8x = 16

Name Algebra 1 Midterm Review Period. = 10 4x e) x ) Solve for y: a) 6x 3y = 12 b) 4y 8x = 16 Name Algebra 1 Date Midterm Review Period 1) Solve each equation: a) x 2x + 2 = 3 b) 5 5 + 9 = 13 c) 64 = 9x +1 d) x 7 2 = 10 4x e) x + 2 3 = 3x 2) Solve for y: a) 6x 3y = 12 b) 4y 8x = 16 3) Solve and

More information

Unit 5 Test Review Systems of Linear Equations Name Class Date

Unit 5 Test Review Systems of Linear Equations Name Class Date Unit 5 Test Review Systems of Linear Equations Name Class Date Find the mistake - The following problems have been solved HOWEVER there could be a mistake. Each question is worth 3 points: 1pt the mistake,

More information

28 (Late Start) 7.2a Substitution. 7.1b Graphing with technology Feb 2. 4 (Late Start) Applications/ Choosing a method

28 (Late Start) 7.2a Substitution. 7.1b Graphing with technology Feb 2. 4 (Late Start) Applications/ Choosing a method Unit 7: Systems of Linear Equations NAME: The calendar and all assignments are subject to change. Students will be notified of any changes during class, so it is their responsibility to pay attention and

More information

Name. Check with teacher. equation: a. Can you find. a. (-2, -3) b. (1, 3) c. (2, 5) d. (-2, -6) a. (-2, 6) b. (-1, 1) c. (1, 3) d. (0, 0) Explain why

Name. Check with teacher. equation: a. Can you find. a. (-2, -3) b. (1, 3) c. (2, 5) d. (-2, -6) a. (-2, 6) b. (-1, 1) c. (1, 3) d. (0, 0) Explain why 7.1 Solving Systems of Equations: Graphing Name Part I - Warm Up with ONE EQUATION: a. Which of the following is a solution to the equation: y 3x 1? a. (-2, -3) b. (1, 3) c. (2, 5) d. (-2, -6) Partt II

More information

UNIT 5 INEQUALITIES CCM6+/7+ Name: Math Teacher:

UNIT 5 INEQUALITIES CCM6+/7+ Name: Math Teacher: UNIT 5 INEQUALITIES 2015-2016 CCM6+/7+ Name: Math Teacher: Topic(s) Page(s) Unit 5 Vocabulary 2 Writing and Graphing Inequalities 3 8 Solving One-Step Inequalities 9 15 Solving Multi-Step Inequalities

More information

Writing and Solving Equations

Writing and Solving Equations Writing and Solving Equations Melody s Music Solution Lesson 6-1 Modeling and Writing Two-Step Equations ACTIVITY 6 Learning Targets: Use variables to represent quantities in real-world problems. Model

More information

8 th Grade Domain 2: Algebra and Functions (40%) Sara

8 th Grade Domain 2: Algebra and Functions (40%) Sara 8 th Grade Domain 2: Algebra and Functions (40%) 1. Tara creates a budget for her weekly expenses. The graph shows how much money is in the account at different times. Find the slope of the line and tell

More information

Why? Speed Skating Tracks offi cial track short track

Why? Speed Skating Tracks offi cial track short track Applying Systems of Linear Equations Then You solved systems of equations by using substitution and elimination. (Lessons 6-2, 6-3, and 6-4) Now 1Determine the best method for solving systems of 2Apply

More information

Unit 12: Systems of Equations

Unit 12: Systems of Equations Section 12.1: Systems of Linear Equations Section 12.2: The Substitution Method Section 12.3: The Addition (Elimination) Method Section 12.4: Applications KEY TERMS AND CONCEPTS Look for the following

More information

Algebra I Solving & Graphing Inequalities

Algebra I Solving & Graphing Inequalities Slide 1 / 182 Slide 2 / 182 Algebra I Solving & Graphing Inequalities 2016-01-11 www.njctl.org Slide 3 / 182 Table of Contents Simple Inequalities Addition/Subtraction click on the topic to go to that

More information

1. What are the various types of information you can be given to graph a line? 2. What is slope? How is it determined?

1. What are the various types of information you can be given to graph a line? 2. What is slope? How is it determined? Graphing Linear Equations Chapter Questions 1. What are the various types of information you can be given to graph a line? 2. What is slope? How is it determined? 3. Why do we need to be careful about

More information

Systems of Equations Unit Five ONE NONE INFINITE

Systems of Equations Unit Five ONE NONE INFINITE Systems of Equations Unit Five ONE NONE INFINITE Standards: 8.EE.8 Analyze and solve pairs of simultaneous linear equations. a. Understand that solutions to a system of two linear equations in two variables

More information

3. Find the area for each question below. a. (3x 2)(2x + 5) b. 4. Simplify the expressions below. is equal to 1, what is the value of a?

3. Find the area for each question below. a. (3x 2)(2x + 5) b. 4. Simplify the expressions below. is equal to 1, what is the value of a? Permitted resources: 2018 2019 Algebra 1 Midterm Review FSA Approved calculator Algebra 1 FSA Reference Sheet 1. The expression 13x + 5 represents the number of marbles you have after shopping at the game

More information

Algebra 2 Level 2 Summer Packet

Algebra 2 Level 2 Summer Packet Algebra Level Summer Packet This summer packet is for students entering Algebra Level for the Fall of 01. The material contained in this packet represents Algebra 1 skills, procedures and concepts that

More information

Final Exam Study Guide

Final Exam Study Guide Algebra 2 Alei - Desert Academy 2011-12 Name: Date: Block: Final Exam Study Guide 1. Which of the properties of real numbers is illustrated below? a + b = b + a 2. Convert 6 yards to inches. 3. How long

More information

6 which of the following equations would give you a system of equations with the same line and infinitely many solutions?

6 which of the following equations would give you a system of equations with the same line and infinitely many solutions? Algebra 1 4 1 Worksheet Name: Per: Part I: Solve each system of equations using the graphing method. 1) y = x 5 ) -x + y = 6 y = x + 1 y = -x 3) y = 1 x 3 4) 4x y = 8 y = 1 x + 1 y = x + 3 5) x + y = 6

More information

Solve each absolute value equation x 7 = x 9 = (3x 12) = - 12

Solve each absolute value equation x 7 = x 9 = (3x 12) = - 12 Solve each absolute value equation. 16. 3x 7 = 11 17. - 4 x 9 = - 16 18. 2(3x 12) = - 12 19. Explain why there can be one, two or no solutions to an absolute value equation. 5. Solve each equation for

More information

ALGEBRA UNIT 5 LINEAR SYSTEMS SOLVING SYSTEMS: GRAPHICALLY (Day 1)

ALGEBRA UNIT 5 LINEAR SYSTEMS SOLVING SYSTEMS: GRAPHICALLY (Day 1) ALGEBRA UNIT 5 LINEAR SYSTEMS SOLVING SYSTEMS: GRAPHICALLY (Day 1) System: Solution to Systems: Number Solutions Exactly one Infinite No solution Terminology Consistent and Consistent and Inconsistent

More information

3. Find the area of each rectangle shown below. 4. Simplify the expressions below. 5. If the expression 3a 2 9. is equal to 3, what is the value of d?

3. Find the area of each rectangle shown below. 4. Simplify the expressions below. 5. If the expression 3a 2 9. is equal to 3, what is the value of d? Permitted resources: 2018 2019 Algebra 1 Midterm Review FSA Approved calculator Algebra 1 FSA Reference Sheet 1. The expression 13x + 5 represents the number of marbles you have after purchasing 13 bags

More information

Section 2.2 Objectives

Section 2.2 Objectives Section 2.2 Objectives Solve multi-step equations using algebra properties of equality. Solve equations that have no solution and equations that have infinitely many solutions. Solve equations with rational

More information

CC Math I UNIT 7 Systems of Equations and Inequalities

CC Math I UNIT 7 Systems of Equations and Inequalities CC Math I UNIT 7 Systems of Equations and Inequalities Name Teacher Estimated Test Date MAIN CONCEPTS Page(s) Study Guide 1 2 Equations of Circles & Midpoint 3 5 Parallel and Perpendicular Lines 6 8 Systems

More information

Foundations of Math. Chapter 3 Packet. Table of Contents

Foundations of Math. Chapter 3 Packet. Table of Contents Foundations of Math Chapter 3 Packet Name: Table of Contents Notes #43 Solving Systems by Graphing Pg. 1-4 Notes #44 Solving Systems by Substitution Pg. 5-6 Notes #45 Solving by Graphing & Substitution

More information

Inequalities Chapter Test

Inequalities Chapter Test Inequalities Chapter Test Part 1: For questions 1-9, circle the answer that best answers the question. 1. Which graph best represents the solution of 8 4x < 4 A. B. C. D. 2. Which of the following inequalities

More information

Consistent and Dependent

Consistent and Dependent Graphing a System of Equations System of Equations: Consists of two equations. The solution to the system is an ordered pair that satisfies both equations. There are three methods to solving a system;

More information

Keystone Exam Concept Review. Properties and Order of Operations. Linear Equations and Inequalities Solve the equations. 1)

Keystone Exam Concept Review. Properties and Order of Operations. Linear Equations and Inequalities Solve the equations. 1) Keystone Exam Concept Review Name: Properties and Order of Operations COMMUTATIVE Property of: Addition ASSOCIATIVE Property of: Addition ( ) ( ) IDENTITY Property of Addition ZERO PRODUCT PROPERTY Let

More information

Name: Systems 2.1. Ready Topic: Determine if given value is a solution and solve systems of equations

Name: Systems 2.1. Ready Topic: Determine if given value is a solution and solve systems of equations Name: Systems 2.1 Ready, Set, Go! Ready Topic: Determine if given value is a solution and solve systems of equations TE-16 1. Graph both equations on the same axes. Then determine which ordered pair is

More information

Algebra 1 Fall Review

Algebra 1 Fall Review Name Algebra 1 Fall Review 2013-2014 Date 1. Write an inequality to best represent the graph shown at right. (A.1.D.) m: b: inequality: 2. Write an inequality to best describe the graph shown at right.

More information

a. Bob: 7, Bridget: 4, Brian 1 b. Bob: 7, Bridget: 4, Brian 3 c. Bob: 7, Bridget: 14, Brian 3 a. 100 b. 150 c c. 2 d.

a. Bob: 7, Bridget: 4, Brian 1 b. Bob: 7, Bridget: 4, Brian 3 c. Bob: 7, Bridget: 14, Brian 3 a. 100 b. 150 c c. 2 d. Period: Date: K. Williams 8th Grade Year Review: Chapters -4. A neighborhood pool charges $22 for a pool membership plus an additional $2 for each visit to the pool. If Elliot visited the pool 6 times,

More information

Intensive Math-Algebra I Mini-Lesson MA.912.A.3.1

Intensive Math-Algebra I Mini-Lesson MA.912.A.3.1 Intensive Math-Algebra I Mini-Lesson MA.912.A.3.1 Summer 2013 Solving Linear Equations Student Packet Day 3 Name: Date: Benchmark MA.912.A.3.1 Solve linear equations in one variable that include simplifying

More information

Name Class Date. What is the solution to the system? Solve by graphing. Check. x + y = 4. You have a second point (4, 0), which is the x-intercept.

Name Class Date. What is the solution to the system? Solve by graphing. Check. x + y = 4. You have a second point (4, 0), which is the x-intercept. 6-1 Reteaching Graphing is useful for solving a system of equations. Graph both equations and look for a point of intersection, which is the solution of that system. If there is no point of intersection,

More information

Algebra I. Systems of Linear Equations and Inequalities. Slide 1 / 179. Slide 2 / 179. Slide 3 / 179. Table of Contents

Algebra I. Systems of Linear Equations and Inequalities. Slide 1 / 179. Slide 2 / 179. Slide 3 / 179. Table of Contents Slide 1 / 179 Algebra I Slide 2 / 179 Systems of Linear Equations and Inequalities 2015-04-23 www.njctl.org Table of Contents Slide 3 / 179 Click on the topic to go to that section 8th Grade Review of

More information

Unit 2 Solving Equations & Inequalities

Unit 2 Solving Equations & Inequalities Coordinate Algebra Unit Solving Equations & Inequalities Name: Date: Unit Review Solve each system of linear equations by the given method. 1. Solve by Substitution: 5y 9 x y. Solve by Substitution: 15y

More information

Algebra 1 PAP Fall Exam Review

Algebra 1 PAP Fall Exam Review Name: Pd: 2016-2017 Algebra 1 PAP Fall Exam Review 1. A collection of nickels and quarters has a value of $7.30. The value of the quarters is $0.80 less than triple the value of the nickels. Which system

More information

Unit 6 Systems of Equations

Unit 6 Systems of Equations 1 Unit 6 Systems of Equations General Outcome: Develop algebraic and graphical reasoning through the study of relations Specific Outcomes: 6.1 Solve problems that involve systems of linear equations in

More information

Name Per. Keystone Exams Practice Test A.) $300,000 B.) $400,000 C.) $500,000 D.) $600,000

Name Per. Keystone Exams Practice Test A.) $300,000 B.) $400,000 C.) $500,000 D.) $600,000 Name Per Basic Skills Keystone Exams Practice Test 1.) A theme park charges $52 for a day pass and $110 for a week pass. Last month, 4,432 day passes and 979 week passes were sold. Which of the following

More information

Additional Exercises 5.1 Form I

Additional Exercises 5.1 Form I Additional Exercises 5.1 Form I Solving Systems of Linear Equations by Graphing Determine whether the given ordered pair is a solution of the system. 1. (5, ) 1. x + y = 7 x y = 3. ( 1, ). x + y = 5 x

More information

4. Based on the table below, what is the joint relative frequency of the people surveyed who do not have a job and have a savings account?

4. Based on the table below, what is the joint relative frequency of the people surveyed who do not have a job and have a savings account? Name: Period: Date: Algebra 1 Common Semester 1 Final Review Like PS4 1. How many surveyed do not like PS4 and do not like X-Box? 2. What percent of people surveyed like the X-Box, but not the PS4? 3.

More information

4) Solve for this system using your graphing

4) Solve for this system using your graphing Algebra Unit 5 HW Day 1 SOLVING GRAPHICALLY Graph the following systems: 1) x 2y 12 y 2x 6 2) y x 2 6x 2y 10 ) x y 9 4) Solve for this system using your graphing x calculator. [You will still need to put

More information

Algebra 1 Keystone Remediation Packet Module 1 Anchor 2

Algebra 1 Keystone Remediation Packet Module 1 Anchor 2 Algebra 1 Keystone Remediation Packet Module 1 Anchor 2 A.1.1.2.1.1 Write, solve, and/or graph linear equations using various methods. A.1.1.2.1.2 Use and/or identify an algebraic property to justify any

More information

NAME DATE PERIOD. Graphing Equations in Slope-Intercept Form

NAME DATE PERIOD. Graphing Equations in Slope-Intercept Form NAME DATE PERID 4-1 Skills Practice Graphing Equations in Slope-Intercept Form Write an equation of a line in slope-intercept form with the given slope and -intercept. 1. slope: 5, -intercept: -3. slope:

More information

Reteaching Using Deductive and Inductive Reasoning

Reteaching Using Deductive and Inductive Reasoning Name Date Class Reteaching Using Deductive and Inductive Reasoning INV There are two types of basic reasoning in mathematics: deductive reasoning and inductive reasoning. Deductive reasoning bases a conclusion

More information

4. The table shows the number of toll booths driven through compared to the cost of using a Toll Tag.

4. The table shows the number of toll booths driven through compared to the cost of using a Toll Tag. ALGEBRA 1 Fall 2016 Semester Exam Review Name 1. According to the data shown below, which would be the best prediction of the average cost of a -bedroom house in Georgetown in the year 2018? Year Average

More information

Sample. Test Booklet. Subject: MA, Grade: HS PSSA 2013 Keystone Algebra 1. - signup at to remove - Student name:

Sample. Test Booklet. Subject: MA, Grade: HS PSSA 2013 Keystone Algebra 1. - signup at   to remove - Student name: Test Booklet Subject: MA, Grade: HS PSSA 2013 Keystone Algebra 1 Student name: Author: Pennsylvania District: Pennsylvania Released Tests Printed: Friday May 31, 2013 1 Which of the following inequalities

More information

LHS June 2012 Algebra 1 Final Exam

LHS June 2012 Algebra 1 Final Exam Teacher: (circle one) Mrs. Gordon Mr. Normile E-block Mr. Normile F-block LHS June 2012 Algebra 1 Final Exam Multiple Choice + Short Answer = /65 Part I Multiple Choice 33 questions 33 points This is a

More information

Math 1 Unit 7 Review

Math 1 Unit 7 Review Name: ate: 1. Which ordered pair is the solution to this system of equations? 5. system of equations is graphed on the set of axes below. y = x + 4 x + y = 2. (1, 5). (0, 2). ( 1, 3). ( 4, 0) 2. Which

More information

Define the word inequality

Define the word inequality Warm Up: Define the word inequality Agenda: Objective- Students can solve linear inequalities in one variable, including equations with coefficients represented by letters. Define Inequalities One & Two

More information

4. Based on the table below, what is the joint relative frequency of the people surveyed who do not have a job and have a savings account?

4. Based on the table below, what is the joint relative frequency of the people surveyed who do not have a job and have a savings account? Name: Period: Date: Algebra 1 Common Semester 1 Final Review 1. How many surveyed do not like PS4 and do not like X-Box? 2. What percent of people surveyed like the X-Box, but not the PS4? 3. What is the

More information

Simple Inequalities Involving Addition and Subtraction. Unit 3 Inequalities.notebook. November 18, Table of Contents

Simple Inequalities Involving Addition and Subtraction. Unit 3 Inequalities.notebook. November 18, Table of Contents Table of Contents Simple Inequalities Addition/Subtraction Simple Inequalities Multiplication/Division Two-Step and Multiple-Step Inequalities Solving Compound Inequalities Special Cases of Compound Inequalities

More information

Name Class Date. You can use the properties of equality to solve equations. Subtraction is the inverse of addition.

Name Class Date. You can use the properties of equality to solve equations. Subtraction is the inverse of addition. 2-1 Reteaching Solving One-Step Equations You can use the properties of equality to solve equations. Subtraction is the inverse of addition. What is the solution of + 5 =? In the equation, + 5 =, 5 is

More information

Warm Up. Unit #1: Basics of Algebra

Warm Up. Unit #1: Basics of Algebra 1) Write an equation of the given points ( 3, 4) & (5, 6) Warm Up 2) Which of the following choices is the Associative Property 1) 4(x + 2) = 4x + 8 2) 4 + 5 = 5 + 4 3) 5 + ( 5) = 0 4) 4 + (3 + 1) = (4

More information

Math 803. Unit 1: Solving Equations in One Variable (8.EE.7) Part 2

Math 803. Unit 1: Solving Equations in One Variable (8.EE.7) Part 2 Math 803 Unit 1: Solving Equations in One Variable (8.EE.7) Part 2 1.4 Variables on both sides (2.4 text) 1.5 Solve multi-step equations (2.5 text) Name: Period: Teacher s Name: 1 Lesson 1.4 Equations

More information

The Top 11 Keystones of Algebra 1

The Top 11 Keystones of Algebra 1 The Top 11 Keystones of Algebra 1 The Top Eleven Keystones of Algebra 1 You should be able to 1) Simplify a radical expression. 2) Solve an equation. 3) Solve and graph an inequality on a number line.

More information

Algebra Practice Set. *Evaluate number and algebraic expressions using rational numbers and Order of Operations

Algebra Practice Set. *Evaluate number and algebraic expressions using rational numbers and Order of Operations Algebra Practice Set Expressions *Evaluate number and algebraic expressions using rational numbers and Order of Operations *Translate algebraic expressions into words using appropriate language *Write

More information

Name: Class: Date: ID: A

Name: Class: Date: ID: A Name: Class: Date: 8th Grade Advanced Topic III, Linear Equations and Systems of Linear Equations, MA.8.A.1.1, MA.8.1.1.2, MA.8.A.1.3, *MA.8.A.1.4, MA.8.A.1.5, MA.8.A.1.6 Multiple Choice Identify the choice

More information

3-1 Solving Systems of Equations. Solve each system of equations by using a table. 1. ANSWER: (3, 5) ANSWER: (2, 7)

3-1 Solving Systems of Equations. Solve each system of equations by using a table. 1. ANSWER: (3, 5) ANSWER: (2, 7) Solve each system of equations by using a table. 1. 9. CCSS MODELING Refer to the table below. (3, 5) 2. (2, 7) Solve each system of equations by graphing. 3. a. Write equations that represent the cost

More information

REVIEW Algebra 1 Fall Final

REVIEW Algebra 1 Fall Final 1. (A.5A) Solve: 4(x 8) = 4x (7x 3) A. x = 29/7 B. x = 5 C. x = no solution D. x = 5 Use the graph below to answer questions #2-3 6. (A.2E) Write the equation of a line passing through ( 5, 7)that is parallel

More information

Name Date PD. Systems of Equations and Inequalities

Name Date PD. Systems of Equations and Inequalities Name Date PD Sstems of Equations and Inequalities Sstems of Equations Vocabular: A sstem of linear equations is A solution of a sstem of linear equations is Points of Intersection (POI) are the same thing

More information

Grade 8. Functions 8.F.1-3. Student Pages

Grade 8. Functions 8.F.1-3. Student Pages THE NEWARK PUBLIC SCHOOLS THE OFFICE OF MATHEMATICS Grade 8 Functions 8.F.1-3 Student Pages 2012 2012 COMMON CORE CORE STATE STATE STANDARDS ALIGNED ALIGNED MODULES Grade 8 - Lesson 1 Introductory Task

More information

Introduction to Systems of Equations

Introduction to Systems of Equations Systems of Equations 1 Introduction to Systems of Equations Remember, we are finding a point of intersection x 2y 5 2x y 4 1. A golfer scored only 4 s and 5 s in a round of 18 holes. His score was 80.

More information

The graphs intersect. Therefore, there is one solution. The. The solution is (3, 1). many solutions.

The graphs intersect. Therefore, there is one solution. The. The solution is (3, 1). many solutions. Answers (Lesson 7-) Lesson 7-7- NAME DATE PERID Stud Guide and Intervention Graphing Sstems of Equations Number of Solutions Two or more linear equations involving the same variables form a sstem of equations.

More information

Review: Expressions and Equations

Review: Expressions and Equations Review: Expressions and Equations Expressions Order of Operations Combine Like Terms Distributive Property Equations & Inequalities Graphs and Tables Independent/Dependent Variables Constant: a number

More information

To determine the slope or rate of change of a linear function, use m =, positive slopes, rises from left to right, negative

To determine the slope or rate of change of a linear function, use m =, positive slopes, rises from left to right, negative Common Core Regents Review Linear Functions The standard form for a linear equation is y = mx + b, where m represents the slope and b represents the y-intercept. To determine the slope or rate of change

More information

Why? Step 3 Substitute the value from Step 2 into either equation, and solve for the other variable. Write the solution as an ordered pair.

Why? Step 3 Substitute the value from Step 2 into either equation, and solve for the other variable. Write the solution as an ordered pair. Substitution Then You solved systems of equations by graphing. (Lesson 6-1) Now 1Solve systems of equations by using substitution. 2Solve real-world problems involving systems of equations by using substitution.

More information

Name. Algebra I Period

Name. Algebra I Period Name Algebra I Period 1 Simplify the following expression: 1 (8 2 4) 8 4 2 4 4 In slope-intercept form, what is the equation of a line with an x-intercept of -3 and a y-intercept of 5? Record your answer

More information

ALGEBRA UNIT 5 -SYSTEMS SOLVING SYSTEMS: GRAPHICALLY (Day 1)

ALGEBRA UNIT 5 -SYSTEMS SOLVING SYSTEMS: GRAPHICALLY (Day 1) ALGEBRA UNIT 5 -SYSTEMS SOLVING SYSTEMS: GRAPHICALLY (Day 1) System: Solution to Systems: Number Solutions Exactly one Infinite No solution Terminology Consistent and Consistent and Inconsistent independent

More information

Pre-Algebra Semester 1 Practice Exam B DRAFT

Pre-Algebra Semester 1 Practice Exam B DRAFT . Evaluate x y 5 6 80 when x = 0 and y =.. Which expression is equivalent to? + + + +. In Pre-Algebra class, we follow the order of operations in evaluating expressions. Which operation should a student

More information

Coordinate Algebra A Final Exam Review

Coordinate Algebra A Final Exam Review Class: Date: Coordinate Algebra A Final Exam Review Multiple Choice Identify the choice that best completes the statement or answers the question. Do NOT write on the test. You may use your calculator.

More information

Algebra I. Systems of Linear Equations and Inequalities. 8th Grade Review. Slide 1 / 179 Slide 2 / 179. Slide 4 / 179. Slide 3 / 179.

Algebra I. Systems of Linear Equations and Inequalities. 8th Grade Review. Slide 1 / 179 Slide 2 / 179. Slide 4 / 179. Slide 3 / 179. Slide 1 / 179 Slide 2 / 179 lgebra I Systems of Linear Equations and Inequalities 2015-04-23 www.njctl.org Slide 3 / 179 Table of Contents Click on the topic to go to that section 8th Grade Review of Systems

More information

ALGEBRA 1 SEMESTER 1 INSTRUCTIONAL MATERIALS Courses: Algebra 1 S1 (#2201) and Foundations in Algebra 1 S1 (#7769)

ALGEBRA 1 SEMESTER 1 INSTRUCTIONAL MATERIALS Courses: Algebra 1 S1 (#2201) and Foundations in Algebra 1 S1 (#7769) Multiple Choice: Identify the choice that best completes the statement or answers the question. 1. Ramal goes to the grocery store and buys pounds of apples and pounds of bananas. Apples cost dollars per

More information

How can you use linear functions of two independent variables to represent problem situations?

How can you use linear functions of two independent variables to represent problem situations? Problems that occur in business situations often require expressing income as a linear function of one variable like time worked or number of sales. For example, if an employee earns $7.25 per hour, then

More information

Ready To Go On? Skills Intervention 2-1 Solving Equations by Adding or Subtracting

Ready To Go On? Skills Intervention 2-1 Solving Equations by Adding or Subtracting Ready To Go On? Skills Intervention 2-1 Solving Equations by Adding or Subtracting Find these vocabulary words in Lesson 2-1 and the Multilingual Glossary. Vocabulary equation solution of an equation Solve

More information

spring98a Math A Regents Exam Test Sampler spring ) ) 2.5

spring98a Math A Regents Exam Test Sampler spring ) ) 2.5 spring98a For what value of x will 8 and x have the same mean (average) as 27 and 5? ).5 2) 8 3) 24 4) 40 6 Which is a factor of x 2 + 5x 24? ) (x + 4) 2) (x 4) 3) (x + 3) 4) (x 3) 2 If 2x = 4(x + 5),

More information

1. The sum of four consecutive even numbers is 52. What is the largest of these numbers?

1. The sum of four consecutive even numbers is 52. What is the largest of these numbers? 1. The sum of four consecutive even numbers is 52. What is the largest of these numbers? 26 22 C 16 10 2. In a high school basketball game, Sarah scored 10 points in the first half of the game. In the

More information

Algebra 1 Midterm Review

Algebra 1 Midterm Review Name Block Algebra 1 Midterm Review MULTIPLE CHOICE Write the letter for the correct answer at the left of each question. 1. Solve: A. 8 C. 2. Solve: A. 43 C. 42 3. Solve the compound inequality and graph

More information

Equations can be classified according to the types of operations and quantities involved. Important types include:

Equations can be classified according to the types of operations and quantities involved. Important types include: UNIT 5. EQUATIONS AND SYSTEM OF EQUATIONS EQUATIONS An equation is a mathematical statement that asserts the equality of two expressions. In modern notation, this is written by placing the expressions

More information

Indiana Core 40 End-of-Course Assessment Algebra I Blueprint*

Indiana Core 40 End-of-Course Assessment Algebra I Blueprint* Types of items on the Algebra I End-of-Course Assessment: Multiple-choice 1 point per problem The answer to the question can be found in one of four answer choices provided. Numeric response 1 point per

More information

Math 1 Variable Manipulation Part 4 Word Problems

Math 1 Variable Manipulation Part 4 Word Problems Math 1 Variable Manipulation Part 4 Word Problems 1 TRANSLATING FROM ENGLISH INTO ALGEBRA (PLUG IN) The next part of variable manipulation problems is to figure out the problem from real life situations.

More information

Part 1 1 st 6weeks material

Part 1 1 st 6weeks material Name Date Period Part 1 1 st 6weeks material 1. Write an expression that can be used to determine the number of blocks in the n th figure. 2. Write an expression to represent the sequence below: 5, 8,

More information

Algebra QBA 1 Review. 4. Solve. Check your answer. 5. Solve. Check your answer. 6. Solve 14 + s = 32.

Algebra QBA 1 Review. 4. Solve. Check your answer. 5. Solve. Check your answer. 6. Solve 14 + s = 32. Algebra QBA 1 Review Short Answer 1. Juan scored 26 points in the first half of the basketball game, and he scored n points in the second half of the game. Write an expression to determine the number of

More information

Algebra. Chapter 6: Systems of Equations and Inequalities. Name: Teacher: Pd:

Algebra. Chapter 6: Systems of Equations and Inequalities. Name: Teacher: Pd: Algebra Chapter 6: Systems of Equations and Inequalities Name: Teacher: Pd: Table of Contents Chapter 6-1: SWBAT: Identify solutions of systems of linear equations in two variables; Solve systems of linear

More information

Algebra I Final Study Guide

Algebra I Final Study Guide 2011-2012 Algebra I Final Study Guide Short Answer Source: www.cityoforlando.net/public_works/stormwater/rain/rainfall.htm 1. For which one month period was the rate of change in rainfall amounts in Orlando

More information

Evaluate and Simplify Algebraic Expressions

Evaluate and Simplify Algebraic Expressions TEKS 1.2 a.1, a.2, 2A.2.A, A.4.B Evaluate and Simplify Algebraic Expressions Before You studied properties of real numbers. Now You will evaluate and simplify expressions involving real numbers. Why? So

More information

Solving and Graphing Linear Inequalities Chapter Questions. 2. Explain the steps to graphing an inequality on a number line.

Solving and Graphing Linear Inequalities Chapter Questions. 2. Explain the steps to graphing an inequality on a number line. Solving and Graphing Linear Inequalities Chapter Questions 1. How do we translate a statement into an inequality? 2. Explain the steps to graphing an inequality on a number line. 3. How is solving an inequality

More information

IM1: UNIT 3. HOMEWORK PACKET

IM1: UNIT 3. HOMEWORK PACKET IM1: UNIT 3. HOMEWORK PACKET Week 1 Name: Period: Day 1: Write an equation for each situation. Then solve the equation. Show your work. 1) DVDs bought online cost $12 each, plus a shipping fee of $5. The

More information

Mathematics Department Columbia High School. Advanced Algebra 2 Summer Packet

Mathematics Department Columbia High School. Advanced Algebra 2 Summer Packet Mathematics Department Columbia High School Advanced Algebra Summer Packet This summer packet is for students entering Advanced Algebra (10-5) for the Fall. The material contained in this packet represents

More information

Module 1-A Linear Inequalities. C. x > 3 D. x < 3 A. 4.4 B. 4.5 C. 4.6 D. 4.7

Module 1-A Linear Inequalities. C. x > 3 D. x < 3 A. 4.4 B. 4.5 C. 4.6 D. 4.7 Name: Date: 1. The inequality 3x + 2 > x + 8 is equivalent to. x > 3 2. x > 3 2 C. x > 3 D. x < 3 2. The inequality 2x > x + 7 is equivalent to. x > 7. x < 7 C. x = 7 D. x > 7 3 3. Which number is not

More information

Fall IM I Exam B

Fall IM I Exam B Fall 2011-2012 IM I Exam B Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which of the following equations is linear? a. y = 2x - 3 c. 2. What is the

More information

Unit 5 SIMULTANEOUS LINEAR EQUATIONS

Unit 5 SIMULTANEOUS LINEAR EQUATIONS MATH 8 Unit 5 SIMULTANEOUS LINEAR EQUATIONS By the end of this unit, students should be able to: 1. Solve simultaneous linear equations by graphing. 2. Understand what it means to solve a system of equations.

More information

Section 4 Topic 1 Arithmetic Sequences

Section 4 Topic 1 Arithmetic Sequences Section 4 Topic 1 Arithmetic Sequences Let s look at the following sequence of numbers: 3, 8, 13, 18, 23,.... Ø Ø Ø The at the end means that this sequence goes on forever. 3, 8, 13, 18, and 23 are the

More information

Geometry Pre-Test. Name: Class: Date: ID: A. Multiple Choice Identify the choice that best completes the statement or answers the question.

Geometry Pre-Test. Name: Class: Date: ID: A. Multiple Choice Identify the choice that best completes the statement or answers the question. Class: Date: Geometry Pre-Test Multiple Choice Identify the choice that best completes the statement or answers the question. 1. An equilateral triangle has three sides of equal length. What is the equation

More information

STANDARDS OF LEARNING CONTENT REVIEW NOTES. ALGEBRA I Part II 1 st Nine Weeks,

STANDARDS OF LEARNING CONTENT REVIEW NOTES. ALGEBRA I Part II 1 st Nine Weeks, STANDARDS OF LEARNING CONTENT REVIEW NOTES ALGEBRA I Part II 1 st Nine Weeks, 2016-2017 OVERVIEW Algebra I Content Review Notes are designed by the High School Mathematics Steering Committee as a resource

More information

Linear Functions. Unit 3

Linear Functions. Unit 3 Linear Functions Unit 3 Standards: 8.F.1 Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and

More information