What is the solution of the system? Use a graph

Name: ______________________ Class: _________________ Date: _________ ID: A

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SREB UNIT 5 TEST STUDY GUIDE

Multiple ChoiceIdentify the choice that best completes the statement or answers the question.

What is the solution of the system? Use a graph.

____ 1. y = –2x + 3y = 3x – 3a. c.

b. d.

How many solutions does the system have?

____ 2. x = −4y − 3−4x − 16y = 12a. one solution c. infinitely many solutionsb. two solutions d. no solution

Name: ______________________ ID: A

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____ 3. y = 5x − 2−5y + 25x = −25a. one solution c. infinitely many solutionsb. two solutions d. no solution

How many solutions does the system have?

____ 4. x + y = −2−2x − 2y = 4a. one solution c. infinitely many solutionsb. two solutions d. no solution

Name: ______________________ ID: A

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____ 5. A local citizen wants to fence a rectangular community garden. The length of the garden should be at least 110 ft, and the distance around should be no more than 380 ft. Write a system of inequalities that models the possible dimensions of the garden. Graph the system to show all possible solutions.a. y ≥ 110

2x + 2y ≤ 380c. y ≤ 110

2x + 2y ≥ 380

b. y ≤ 1102x + 2y ≤ 380

d. y ≥ 1102x + 2y ≥ 380

Name: ______________________ ID: A

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Short Answer - SHOW ALL YOUR WORK!

6. The number of sofas a factory produces varies directly with the number of hours the machinery is operational. Suppose the factory can produce 236 sofas in 40 hours. What is an equation that relates the number of sofas produced, n, with the amount of time, t, in hours? What is the graph of your equation?

7. Giselle pays $200 in advance on her account at the athletic club. Each time she uses the club, $5 is deducted from the account. Model the situation with a linear function and a graph.

8. The table shows the height of an elevator above ground level after a certain amount of time. Model the data with an equation. Let y stand for the height of the elevator in feet and let x stand for the time in seconds.

Time (s) Height (ft)

10 235

20 220

40 190

60 160

Find the x- and y-intercept of the line.

9. 8x + 4y = 56

10. 19

x + 73

y = 4


11. –4x + 3y = –12–2x + 3y = –18

12. y = x + 1y = 5x – 3

13. 4x + 5y = 1−5x + 2y = 7

14. Tom has a collection of 21 CDs and Nita has a collection of 14 CDs. Tom is adding 3 CDs a month to his collection while Nita is adding 4 CDs a month to her collection. Find the number of months after which they will have the same number of CDs.

Name: ______________________ ID: A

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15. The only coins that Alexis has are dimes and quarters. Her coins have a total value of $5.80. She has a total of 40 coins. How many does she have of each coin?


16. y = 5x + 3y = 5x – 2

17. y = x + 2y – 2 = x

What is the solution of the system? Use substitution.

18. 3x + 2y = 7y = –3x + 11

19. 2x − y = −73x − y = −2

20. 8x − 2y = 43x − y = 5

21. The length of a rectangle is 3 centimeters more than 3 times the width. If the perimeter of the rectangle is 46 centimeters, find the dimensions of the rectangle.

22. A corner store sells two kinds of baked goods: cakes and pies. A cake costs $13 and a pie costs $5. In one day, the store sold 14 baked goods for a total of $134. How many cakes did they sell?

What is the solution of the system? Use elimination.

23. 2x + 3y = 24x – 3y = 22

24. 9x − y = 9−3x + y = 9

25. 3x – 4y = 9–3x + 2y = 9

26. Sharon has some one-dollar bills and some five-dollar bills. She has 14 bills. The value of the bills is $30. Solve a system of equations using elimination to find how many of each kind of bill she has.

27. The school cafeteria sells two kinds of wraps: vegetarian and chicken. The vegetarian wrap costs $1.00 and the chicken wrap costs $3.20. Today they made $244.80 from the 137 wraps sold. How many of the wraps sold were vegetarian?

Name: ______________________ ID: A

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What is the solution of the system? Use any method.

28. 3x – 4y = –24x + y = –1

29. x + 5y = 72x + 20y = 24

30. 5x = 30 + 2y8y = –48 + 2x

31. 10x + 3y = 429x + 8y = 59

32. –3x + 7y = 19–5x – 6y = 14

33. You decide to market your own custom computer software. You must invest $3255 for computer hardware, and spend $2.90 to buy and package each disk. If each program sells for $13.75, how many copies must you sell to break even?

34. Mike and Kim invest $12,000 in equipment to print yearbooks for schools. Each yearbook costs $6 to print and sells for $30. How many yearbooks must they sell before their business breaks even?

35. At the local ballpark, the team charges $5 for each ticket and expects to make $1,200 in concessions. The team must pay its players $1,900 and pay all other workers $1,400. Each fan gets a free bat that costs the team $2 per bat. How many tickets must be sold to break even?

36. The local zoo is filling two water tanks for the elephant exhibit. One water tank contains 34 gal of water and is filled at a constant rate of 10 gal/h. The second water tank contains 19 gal of water and is filled at a constant rate of 5 gal/h. When will the two tanks have the same amount of water? Explain. Let x = the number of hours the tanks are filling and let y = the number of gallons in the tank.

37. The local zoo has two water tanks for the elephant exhibit that are leaking One water tank contains 17 gal of water and is leaking at a constant rate of 3 gal/h. The second water tank contains 5 gal of water and is leaking at a constant rate of 6 gal/h. When will the two tanks have the same amount of water? Explain. Let x = the number of hours the tanks are filling and let y = the number of gallons in the tank.

What is the graph of the system?

38. y ≤ x + 42x + y ≤ −4

39. y ≤ −x − 1y ≥ 2x + 4

Name: ______________________ ID: A

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What system of inequalities is represented by the graph?

40.

41.

42. Is the ordered pair a solution of y > 910

x + 1?

(–9, 9)

Name: ______________________ ID: A

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43. You have a gift certificate to a book store worth $60. Each paperback books is $8 and each hardcover books is $15. You must spend at least $25 in order to use the gift certificate. Write and graph a system of inequalities to model the number of each kind of books you can buy. Let x = the number of paperback books and y = the number of hardback books.

Write the inequalities.

44. Inequality 1: _______________________

45. Inequality 2: ____________________________

Solve for y.

46. Equation 1: _________________________________________________ Step 1

47. Equation 1: _________________________________________________ Answer

48. Equation 2: ______________________________________ Step 1

Name: ______________________ ID: A

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49. Equation 2: _________________________________________________ Answer

Graph the inequalities on the coordinate plane above (Problem 60). Identify the slope m, and y-intercept b below.

50. Inequality 1: m = ______________________

51. Inequality 1: b = ______________________

52. Inequality 2: m = ______________________

53. Inequality 2: b = ______________________

The data provided in the table show the supply and demand for game cartridge at a toy warehouse. Use the table for Problems 69-75.

PRICE SUPPLY DEMAND$20.00 150 500$30.00 250 400$50.00 450 200

54. Write the supply equation as a function of the price using the data in the table. Show your work.

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

55. Write the demand equation as a function of the price using the data in the table. Show your work.

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

Name: ______________________ ID: A

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56. Solve this system of equations to find the equilibrium price. What does your answer mean?.

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

57. On the graph below label the axes and the scale for the data in the table above.

58. On the graph above graph the data points from the table and draw and label the supply line and the demand line.

Name: ______________________ ID: A

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59. Determine the equilibrium point from the graph.

________________________________________

60. How does your anewer in problem 74 compare with your answer from problem 71 in which you found teh equilibrium algebraically?

____________________________________________________________________________________________

ID: A

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SREB UNIT 5 TEST STUDY GUIDEAnswer Section

MULTIPLE CHOICE

1. ANS: A PTS: 1 DIF: L2 REF: 6-1 Solving Systems By Graphing 2. ANS: C PTS: 1 DIF: L3

REF: 6-2 Solving Systems Using Substitution 3. ANS: D PTS: 1 DIF: L3

REF: 6-2 Solving Systems Using Substitution 4. ANS: C PTS: 1 DIF: L3

REF: 6-3 Solving Systems Using Elimination 5. ANS: A PTS: 1 DIF: L3 REF: 6-6 Systems of Linear Inequalities

SHORT ANSWER

6. ANS: n = 5.9t

PTS: 1 DIF: L3 REF: 5-2 Direct Variation

ID: A

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7. ANS:

b = 200 – 5x

PTS: 1 DIF: L3 REF: 5-3 Slope-Intercept Form 8. ANS:

y = −1.5x + 250

PTS: 1 DIF: L3 REF: 5-4 Point-Slope Form 9. ANS:

x-intercept is 7; y-intercept is 14

PTS: 1 DIF: L2 REF: 5-5 Standard Form 10. ANS:

x-intercept is 36; y-intercept is 127

PTS: 1 DIF: L3 REF: 5-5 Standard Form

ID: A

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11. ANS:

PTS: 1 DIF: L3 REF: 6-1 Solving Systems By Graphing 12. ANS:

PTS: 1 DIF: L3 REF: 6-1 Solving Systems By Graphing

ID: A

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13. ANS:


7 months


28 dimes; 12 quarters


no solutions

PTS: 1 DIF: L3 REF: 6-1 Solving Systems By Graphing

ID: A

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17. ANS:

infinitely many solutions


(5, –4)

PTS: 1 DIF: L3 REF: 6-2 Solving Systems Using Substitution 19. ANS:

(5, 17)


(–3, –14)


length = 18 cm; width = 5 cm


8 cakes


(4, –2)

PTS: 1 DIF: L3 REF: 6-3 Solving Systems Using Elimination 24. ANS:

(3, 18)

PTS: 1 DIF: L2 REF: 6-3 Solving Systems Using Elimination

ID: A

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25. ANS: (–9, –9)


4 five-dollar bills, 10 one-dollar bills


88 wraps


(–4, 3)


(2, 1)


(4, –5)


(3, 4)


(–4, 1)


300 copies

PTS: 1 DIF: L3 REF: 6-4 Applications of Linear Systems 34. ANS:

500 yearbooks


700 tickets

PTS: 1 DIF: L3 REF: 6-4 Applications of Linear Systems

ID: A

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36. ANS: They will never have the same amount of water because the solution to the system is (–3,4). It is not possible to have time be –3 hours.


They will never have the same amount of water because the solution to the system is (–4,29). It is not possible to have time be –4 hours.


PTS: 1 DIF: L4 REF: 6-6 Systems of Linear Inequalities 39. ANS:


y ≤ x − 2y ≤ −3x − 6

PTS: 1 DIF: L3 REF: 6-6 Systems of Linear Inequalities

ID: A

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41. ANS: y ≤ x + 83x + y ≥ −8


Yes, 910

(–9) + 1 < 9.

PTS: 1 DIF: L3 REF: 6-5 Linear Inequalities 43. ANS:

8x + 15y ≥ 258x + 15y ≤ 60


7x + 16y ≥ 30

PTS: 1 45. ANS:

7x + 16y ≤ 90

PTS: 1 46. ANS:

7x + 16y = 30 -7x -7x16y = -7x + 30

PTS: 1 47. ANS:

y = (-7x + 30)/16

PTS: 1

ID: A

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48. ANS: 7x + 16y = 90-7x -7x16y = -7x + 90

PTS: 1 49. ANS:

y = (-7x + 90)/16

PTS: 1 50. ANS:

-7/16

PTS: 1 51. ANS:

30/16 = 1.875

PTS: 1 52. ANS:

-7/16

PTS: 1 53. ANS:

90/16 = 5.625

PTS: 1 54. ANS:

m = (250-150)/(30-20) = 10y - 150 = 10(x - 20)y - 150 = 10x - 200y = 10x - 50

PTS: 1 55. ANS:

m = (400-500)/(30-20) = -10y - 500 = -10(x - 20)y - 500 = -10x + 200y = -10x + 700

PTS: 1

ID: A

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56. ANS: S = D10P - 50 = -10P + 700 20P = 750 P = $37.50

IF THE PRICE OF THE GAME CARTRIDGE IS $37.50 THE SUPPLY WILL EXACTLY MEET THE DEMAND OF 325.

PTS: 1 57. ANS:

PTS: 1

ID: A

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58. ANS:

PTS: 1 59. ANS:

(37.50, 325)

PTS: 1 60. ANS:

They are the same.

PTS: 1

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What is the solution of the system? Use a graph