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Systems of Linear Equations

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Unit 6: Systems of Linear Equations and Inequalities

SELECTED RESPONSE
Identify the letter of the choice that best completes the statement or answers the question.

1. Identify the graph that represents the system of linear equations.

[pic]

|A. |[pic] |C. |[pic] |
| | | | |
|B. |[pic] |D. |[pic] |

2. The graph below shows the cost (c), in dollars, to rent a boat for h hours at two different boat companies.

[pic]

At what number of hours will the cost to rent a boat be the same at both companies?

F. 4
G. 5
H. 8
J. 20

3. John and Patrice are each saving money to buy a car. John has $750 saved and will save an additional $30 a week. Patrice has $1,200 saved and will save an additional $20 a week. How many weeks will it take John and Patrice to save the same amount of money?

A. 39 weeks
B. 40 weeks
C. 45 weeks
D. 55 weeks

4. Choose the equation wherein you would isolate a variable easily so that substitution method can be used to solve the linear system.

[pic]

F. Equation 1
G. Equation 2
H. Neither Equation 1 nor Equation 2
J. Both Equation 1 and Equation 2

5. Solve the linear system.
[pic]
A. (5, 7) B. (5, 8) C. (6, 7) D. (6, 8)

6. Which of the following ordered pairs satisfies the linear system?

[pic]

F. (-11, - 5)
G. (-11, 5)
H. (-5, -11)
J. (5, -11)

7. Lindsay earns $7 per hour doing a part time job while George earns $13. They work a total of 9 hours. How many hours does each of them work if they earn a total of $99?

A. Lindsay should work for 3 hours; George should work for 6 hours
B. Lindsay should work for 4 hours; George should work for 5 hours
C. Lindsay should work for 6 hours; George should work for 3 hours
D. Lindsay should work for 7 hours; George should work for 2 hours

8. A shopkeeper sold 24 softballs and basketballs for a sum of $240. The price of a softball is $8 and that of a basketball is $20. How many softballs and basketballs did the shopkeeper sell?

F. 4 softballs, 20 basketballs
G. 12 softballs, 12 basketballs
H. 14 softballs, 10 basketballs
J. 20 softballs, 4 basketballs

9. Which graph corresponds to the linear system that has no solution?

|A. |[pic] |C. |[pic] |
|B. |[pic] |D. |[pic] |

10. Find the number of solutions the linear system has.

[pic]

F. exactly one solution
G. no solution
H. infinitely many solution
J. exactly two solutions

11. Select a system of linear inequalities that describes the shaded region the graph shows.

[pic]

A. [pic]
B. [pic]
C. [pic]
D. [pic]

12. Which graph represents the system of linear inequalities?

[pic]

|F. |[pic] |H. |[pic] |
|G. |[pic] |J. |[pic] |

13. The Perez family is planning a trip to an amusement park. The park has two ticket plans.

• Plan A offers a weekend pass for $12 plus $0.50 per ride.

• Plan B is $1.25 for each ride.

Let x represent the number of rides each person will ride and y represent the cost per person, in dollars. Which of these systems of equations could be used to choose a ticket plan?

A. y = x + 12 y = x + 1.25

B. y = 0.50x y = 1.25x

C. y = 12x + 0.50 y = x + 1.25

D. y = 0.50x + 12 y = 1.25x

STUDENT PRODUCED RESPONSE
Record your answers in the space provided on your answer sheet.

|14. Terry is going to the county fair. She has two choices for purchasing tickets, as shown in the table |[pic] |
|below. | |
| | |
| | |
|Ticket Choices | |
|Admission Price | |
|Cost Per Ride | |
| | |
|A | |
|$6 | |
|$0.50 | |
| | |
|B | |
|$2 | |
|$1.50 | |
| | |
| | |
| | |
| | |
| | |
| | |
|How many rides would Terry have to go on for the total cost of ticket A and ticket B to be equal? | |

|15. At a baseball game Sam bought 2 hamburgers and 1 order of French fries for a total of $5.75. Erica bought |[pic] |
|1 hamburger and 2 orders of French fries for a total of $4.50. What is the cost of one hamburger? Round your | |
|answer to the nearest hundredths. | |

Previous Units

16. Which of the following equations models the relationship between the given and -values shown in the table below?

| | | | | |
| | | | | |

|F. | = + 8 |G. | = 3 + 3 |
|H. | = - - 8 |J. | = 2 + 4 |

17. Solve: -3x +75 = 8x + 20

|A. | 3 |B. |4 |
|C. | 5 |D. |6 |

18. Alice bought a pack of homemade chocolates worth $24 and picked some loose chocolates worth $3 each. How many loose chocolates did she pick, if she spent $39 in all?

|F. |4 |G. |5 |
|H. |6 |J. |7 |

19. Identify the domain and range of the function represented by the mapping.

[pic]

|A. |Domain: {2, - 8, 1, 3}, and Range: {1, 0, 5, 4} |
|B. |Domain: {1, 0, 5, 4}, and Range: {2, - 8, 1, 3} |
|C. |Domain: {0, 5, 4, 1}, and Range: {2, 8, 1, 3} |
|D. |Domain: {2, 8, 1, 3}, and Range: {1, 0, 5, 4} |

|20. Rose wants to order cherries. A box of cherries costs $10.82. What is the maximum number of boxes that|[pic] |
|she can order, if she can spend no more than $35.06 with the shopkeeper charging $2.6 extra for home | |
|delivery? | |

Goal 3

21. The stem and leaf plot below shows Jim’s golf scores.

[pic]

What is the mode of his data?

|A. |1 |
|B. |9 |
|C. |89 |
|D. |99 |

22. If a survey is to be conducted, which of the following is the best way to know the favorite subject of the school students?

|F. |Survey the brilliant students in the school. |
|G. |Survey 15 students from each class. |
|H. |Survey 15 girls from each class. |
|J. |Survey your friends. |

23. The matrix below shows the supplies that are needed to build two different model trucks.

[pic]

How many sheets of plastic are needed to build 17 dump trucks?

|A. |170 |B. |374 |
|C. |544 |D. |595 |

24. Which graph below is not misleading?

[pic]

|F. |Graph 1 |G. |Graph 2 |
|H. |Graph 3 |J. |Graph 4 |

|25. Sam owns a book shop. The box-and-whisker plot shows the number of books he sold Monday through Friday |[pic] |
|last week. | |
| | |
|[pic] | |
| | |
| | |
| | |
|What is the interquartile range (IQR)? | |

Answer Key – Unit 6: Systems of Linear Equations and Inequalities

Current Units 1. B Solving Systems of Linear Equations Indicator: 1.2.3 2. F Solving Systems of Linear Equations Indicator: 1.2.3 3. C Solving Systems of Linear Equations Indicator: 1.2.3 4. G Solving Systems of Linear Equations Indicator: 1.2.3 5. B Solving Systems of Linear Equations Indicator: 1.2.3 6. H Solving Systems of Linear Equations Indicator: 1.2.3 7. A Solving Systems of Linear Equations Indicator: 1.2.3 8. J Solving Systems of Linear Equations Indicator: 1.2.3 9. A Solving Systems of Linear Equations Indicator: 1.2.3 10. G Solving Systems of Linear Equations Indicator: 1.2.3 11. C Solving Systems of Linear Inequalities Indicator: 1.2.3 12. G Solving Systems of Linear Inequalities Indicator: 1.2.3 13. D Solving Systems of Linear Equations Indicator: 1.2.3 14. 4 Solving Systems of Linear Equations Indicator: 1.2.3 15. 2.33 Solving Systems of Linear Equations Indicator: 1.2.3

Previous Units 16. J Linear Functions Indicator: 1.1.2 17. C Solving Equations Indicator: 1.2.1 18. G Linear Functions and Equations Indicator: 1.2.1 19. A Domain and Range Indicator: 1.1.4 20. 3 Solving Inequalities Indicator: 1.2.2

Goal 3 21. C Measures of Central Tendency Indicator: 3.1.2 22. G Survey Techniques Indicator: 3.1.1 23. A Displaying Data with Matrices Indicator: 1.2.5 24. G Misleading Graphs Indicator: 3.2.3 25. 50 Variance: Box-and- Whisker Plot Indicator: 3.1.2

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