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

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Algebra 1 - Ch 7 Practice Test

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

____ 1. What is the solution of the system of equations?y = 3x + 7y = x – 9a. (–1, –10) b. (–17, –8) c. (4, 19) d. (–8, –17)

Graph each system. Tell whether the system has no solution, one solution, or infinitely many solutions.

____ 2. y = 5x – 4y = 5x – 5a. no solutionsb. one solutionc. infinitely many solutions

____ 3. y = x + 4y – 4 = xa. infinitely many solutionsb. no solutionsc. one solution

____ 4. 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.a. length = 5 cm; width = 18 cm c. length = 13 cm; width = 8 cmb. length = 13 cm; width = 5 cm d. length = 18 cm; width = 5 cm

Solve the system of equations using substitution.

____ 5. y = 2x + 3y = 3x + 1a. (–2, –1) b. (–1, –2) c. (2, 7) d. (–2, –5)

____ 6. 3x + 2y = 7y = –3x + 11

a. (6, –3) b. (6, –7) c. −4,192

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d. (5, –4)

____ 7. The sum of two numbers is 82. Their difference is 24. Write a system of equations that describes this situation. Solve by elimination to find the two numbers.a. x + y = 82

x – y = 2448 and 24

c. x + y = 24y – x = 8248 and 30

b. x – y = 82x + y = 2452 and 30

d. x + y = 82x – y = 2453 and 29

Name: ______________________ ID: A

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Solve the system using elimination.

____ 8. 2x – 2y = –8x + 2y = –1a. (–14, 1) b. (1, 5) c. (–3, 1) d. (0, 4)

____ 9. 6x + 3y = –126x + 2y = –4a. (10, –16) b. (2, –8) c. (–2, 8) d. (–10, 16)

____ 10. 5x + 8y = –297x – 2y = –67

a. (–7, 9) b. −10,218

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c. (–1, –3) d. (–9, 2)

____ 11. 3x – 4y = –24x + y = –1a. (–4, 3) b. (0, 6) c. (3, 4) d. (4, 3)

____ 12. By what number should you multiply the first equation to solve using elimination?–3x – 2y = 2–9x + 3y = 24a. 6 b. –9 c. –3 d. 3

____ 13. A jar containing only nickels and dimes contains a total of 60 coins. The value of all the coins in the jar is $4.45. Solve by elimination to find the amount of nickels and dimes that are in the jar.a. 30 nickels and 28 dimes c. 29 nickels and 31 dimesb. 31 nickels and 29 dimes d. 30 nickels and 32 dimes

____ 14. Mrs. Huang operates a soybean farm. She buys many supplies in bulk. Often the bulk products need to be custom mixed before Mrs. Huang can use them. To apply herbicide to a large field she must mix a solution of 67% herbicide with a solution of 46% herbicide to form 42 liters of a 55% solution. How much of the 67% solution must she use?a. 23 L b. 18 L c. 34 L d. 35 L

____ 15. You decide to market your own custom computer software. You must invest $3,255 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? a. 196 copies b. 301 copies c. 300 copies d. 195 copies

____ 16. A motorboat can go 8 miles downstream on a river in 20 minutes. It takes 30 minutes for the boat to go upstream the same 8 miles. Find the speed of the current.a. 20 mph b. 16 mph c. 24 mph d. 4 mph

Name: ______________________ ID: A

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Graph the inequality.

____ 17. y < 4x − 2a. c.

b. d.

Name: ______________________ ID: A

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____ 18. 4x + 6y ≥ 10a. c.

b. d.

Write the linear inequality shown in the graph.

____ 19.

a. y ≤ 3x + 4 b. y ≤ 3x − 4 c. y ≥ 3x − 4 d. y ≥ 3x + 4

Name: ______________________ ID: A

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____ 20. You have $47 to spend at the music store. Each cassette tape costs $5 and each CD costs $10. Write and graph a linear inequality that represents this situation. Let x represent the number of tapes and y the number of CDs.a. 5x + 10y ≥ 47 c. 10x + 5y ≤ 47

b. 10x + 5y ≥ 47 d. 5x + 10y ≤ 47

Find a solution of the system of linear inequalities.

____ 21. y < 3x + 12y ≥ 5x + 7a. (1, 2) b. (0, –1) c. (2, 17) d. (–2, –5)

Name: ______________________ ID: A

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Solve the system of linear inequalities by graphing.

____ 22. y ≤ −x − 1y ≥ 2x + 4a. c.

b. d.

Name: ______________________ ID: A

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Write a system of inequalities for the graph.

____ 23.

a. y ≥ x − 2y ≥ −3x − 6

c. y ≤ x − 2y ≤ −3x − 6

b. y ≤ x + 3y ≥ 2x − 6

d. y ≥ x + 3y ≤ 2x − 6

Name: ______________________ ID: A

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Short Answer

Solve the system of linear inequalities by graphing.

24. y ≤ x + 42x + y ≤ −4

25. SOLVE BY ANY METHOD, SHOW YOUR WORK, AND BOX YOUR ANSWERS

An ice skating arena charges an admission fee for each child plus a rental fee for each pair of ice skates. John paid the admission fees for his six nephews and rented five pairs of ice skates. He was charged $32.00. Juanita paid the admission fees for her seven grandchildren and rented five pairs of ice skates. She was charged $35.25. What is the admission fee? What is the rental fee for a pair of skates?

ID: A

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Algebra 1 - Ch 7 Practice TestAnswer Section

MULTIPLE CHOICE

1. ANS: D DIF: L1 REF: 7-1 Solving Systems By GraphingOBJ: 7-1.1 Solving Systems By Graphing STO: CA 9.0TOP: 7-1 Example 1 KEY: system of linear equations,graphing a system of linear equations MSC: NAEP A4d, NAEP A4g, CAT5.LV19.50, CAT5.LV19.54, IT.LV15.DI, S9.TSK1.PRA, S10.TSK1.PRA, TV.LV19.16, TV.LV19.17, TV.LV19.18, TV.LVALG.55

2. ANS: A DIF: L1 REF: 7-1 Solving Systems By GraphingOBJ: 7-1.2 Analyzing Special Types of Systems STO: CA 9.0TOP: 7-1 Example 3,7-1 Example 4 KEY: system of linear equations,graphing a system of linear equations,no solution,infinitely many solutions MSC: NAEP A4d, NAEP A4g, CAT5.LV19.50, CAT5.LV19.54, IT.LV15.DI, S9.TSK1.PRA, S10.TSK1.PRA, TV.LV19.16, TV.LV19.17, TV.LV19.18, TV.LVALG.55

3. ANS: A DIF: L1 REF: 7-1 Solving Systems By GraphingOBJ: 7-1.2 Analyzing Special Types of Systems STO: CA 9.0TOP: 7-1 Example 3,7-1 Example 4 KEY: system of linear equations,graphing a system of linear equations,no solution,infinitely many solutions MSC: NAEP A4d, NAEP A4g, CAT5.LV19.50, CAT5.LV19.54, IT.LV15.DI, S9.TSK1.PRA, S10.TSK1.PRA, TV.LV19.16, TV.LV19.17, TV.LV19.18, TV.LVALG.55

4. ANS: A DIF: L1 REF: 7-2 Solving Systems Using SubstitutionOBJ: 7-2.1 Using Substitution STO: CA 8.0, CA 9.0 TOP: 7-2 Example 3 KEY: word problem,problem solving,system of linear equations,substitution methodMSC: NAEP A4g, CAT5.LV19.54, IT.LV15.AM, S9.TSK1.PRA, S10.TSK1.PRA, TV.LV19.16, TV.LV19.52, TV.LVALG.54

5. ANS: C DIF: L1 REF: 7-2 Solving Systems Using SubstitutionOBJ: 7-2.1 Using Substitution STO: CA 8.0, CA 9.0 TOP: 7-2 Example 1 KEY: system of linear equations,substitution methodMSC: NAEP A4g, CAT5.LV19.54, IT.LV15.AM, S9.TSK1.PRA, S10.TSK1.PRA, TV.LV19.16, TV.LV19.52, TV.LVALG.54

6. ANS: D DIF: L2 REF: 7-2 Solving Systems Using SubstitutionOBJ: 7-2.1 Using Substitution STO: CA 8.0, CA 9.0 TOP: 7-2 Example 2 KEY: system of linear equations,substitution methodMSC: NAEP A4g, CAT5.LV19.54, IT.LV15.AM, S9.TSK1.PRA, S10.TSK1.PRA, TV.LV19.16, TV.LV19.52, TV.LVALG.54

7. ANS: D DIF: L2 REF: 7-3 Solving Systems Using EliminationOBJ: 7-3.1 Adding or Subtracting to Solve Systems STO: CA 9.0KEY: word problem,problem solving,system of linear equations,elimination method,adding or subtracting equations MSC: NAEP A4g, CAT5.LV19.54, IT.LV15.AM, S9.TSK1.PRA, S10.TSK1.PRA, TV.LV19.16, TV.LV19.49, TV.LV19.52, TV.LVALG.54

ID: A

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8. ANS: C DIF: L1 REF: 7-3 Solving Systems Using EliminationOBJ: 7-3.1 Adding or Subtracting to Solve Systems STO: CA 9.0TOP: 7-3 Example 1 KEY: system of linear equations,elimination method,adding or subtracting equationsMSC: NAEP A4g, CAT5.LV19.54, IT.LV15.AM, S9.TSK1.PRA, S10.TSK1.PRA, TV.LV19.16, TV.LV19.49, TV.LV19.52, TV.LVALG.54

9. ANS: B DIF: L1 REF: 7-3 Solving Systems Using EliminationOBJ: 7-3.1 Adding or Subtracting to Solve Systems STO: CA 9.0TOP: 7-3 Example 1 KEY: system of linear equations,elimination method,adding or subtracting equationsMSC: NAEP A4g, CAT5.LV19.54, IT.LV15.AM, S9.TSK1.PRA, S10.TSK1.PRA, TV.LV19.16, TV.LV19.49, TV.LV19.52, TV.LVALG.54

10. ANS: D DIF: L1 REF: 7-3 Solving Systems Using EliminationOBJ: 7-3.2 Multiplying First to Solve Systems STO: CA 9.0TOP: 7-3 Example 3 KEY: system of linear equations,elimination method,adding or subtracting equationsMSC: NAEP A4g, CAT5.LV19.54, IT.LV15.AM, S9.TSK1.PRA, S10.TSK1.PRA, TV.LV19.16, TV.LV19.49, TV.LV19.52, TV.LVALG.54

11. ANS: A DIF: L1 REF: 7-3 Solving Systems Using EliminationOBJ: 7-3.2 Multiplying First to Solve Systems STO: CA 9.0TOP: 7-3 Example 3 KEY: system of linear equations,elimination method,adding or subtracting equationsMSC: NAEP A4g, CAT5.LV19.54, IT.LV15.AM, S9.TSK1.PRA, S10.TSK1.PRA, TV.LV19.16, TV.LV19.49, TV.LV19.52, TV.LVALG.54

12. ANS: D DIF: L1 REF: 7-3 Solving Systems Using EliminationOBJ: 7-3.2 Multiplying First to Solve Systems STO: CA 9.0TOP: 7-3 Example 3 KEY: system of linear equations,elimination method,adding or subtracting equationsMSC: NAEP A4g, CAT5.LV19.54, IT.LV15.AM, S9.TSK1.PRA, S10.TSK1.PRA, TV.LV19.16, TV.LV19.49, TV.LV19.52, TV.LVALG.54

13. ANS: B DIF: L1 REF: 7-3 Solving Systems Using EliminationOBJ: 7-3.2 Multiplying First to Solve Systems STO: CA 9.0TOP: 7-3 Example 4 KEY: word problem,problem solving,system of linear equations,elimination method,adding or subtracting equations MSC: NAEP A4g, CAT5.LV19.54, IT.LV15.AM, S9.TSK1.PRA, S10.TSK1.PRA, TV.LV19.16, TV.LV19.49, TV.LV19.52, TV.LVALG.54

14. ANS: B DIF: L1 REF: 7-4 Applications of Linear SystemsOBJ: 7-4.1 Writing Systems of Linear Equations STO: CA 9.0TOP: 7-4 Example 1 KEY: word problem,problem solving,system of linear equations,graphing a system of linear equations,substitution method,elimination method,mixture problem MSC: NAEP A4g, CAT5.LV19.54, IT.LV15.AM, S9.TSK1.PRA, S10.TSK1.PRA, TV.LV19.16, TV.LV19.17, TV.LV19.18, TV.LV19.52, TV.LVALG.54

ID: A

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15. ANS: C DIF: L1 REF: 7-4 Applications of Linear SystemsOBJ: 7-4.1 Writing Systems of Linear Equations STO: CA 9.0TOP: 7-4 Example 2 KEY: word problem,problem solving,system of linear equations,graphing a system of linear equations,substitution method,elimination method MSC: NAEP A4g, CAT5.LV19.54, IT.LV15.AM, S9.TSK1.PRA, S10.TSK1.PRA, TV.LV19.16, TV.LV19.17, TV.LV19.18, TV.LV19.52, TV.LVALG.54

16. ANS: D DIF: L2 REF: 7-4 Applications of Linear SystemsOBJ: 7-4.1 Writing Systems of Linear Equations STO: CA 9.0TOP: 7-4 Example 3 KEY: word problem,problem solving,system of linear equations,graphing a system of linear equations,substitution method,elimination method,motion problem MSC: NAEP A4g, CAT5.LV19.54, IT.LV15.AM, S9.TSK1.PRA, S10.TSK1.PRA, TV.LV19.16, TV.LV19.17, TV.LV19.18, TV.LV19.52, TV.LVALG.54

17. ANS: C DIF: L1 REF: 7-5 Linear InequalitiesOBJ: 7-5.1 Graphing Linear Inequalities STO: CA 6.0 TOP: 7-5 Example 1KEY: linear inequality, graphing MSC: NAEP A3a, CAT5.LV19.50, IT.LV15.DI, S9.TSK1.PRA, S10.TSK1.PRA, TV.LV19.16, TV.LVALG.54

18. ANS: D DIF: L2 REF: 7-5 Linear InequalitiesOBJ: 7-5.1 Graphing Linear Inequalities STO: CA 6.0 TOP: 7-5 Example 2KEY: linear inequality, graphing MSC: NAEP A3a, CAT5.LV19.50, IT.LV15.DI, S9.TSK1.PRA, S10.TSK1.PRA, TV.LV19.16, TV.LVALG.54

19. ANS: C DIF: L1 REF: 7-5 Linear InequalitiesOBJ: 7-5.1 Graphing Linear Inequalities STO: CA 6.0 TOP: 7-5 Example 1KEY: linear inequality, graphing MSC: NAEP A3a, CAT5.LV19.50, IT.LV15.DI, S9.TSK1.PRA, S10.TSK1.PRA, TV.LV19.16, TV.LVALG.54

20. ANS: D DIF: L1 REF: 7-5 Linear InequalitiesOBJ: 7-5.2 Modeling Real-World Situations STO: CA 6.0TOP: 7-5 Example 3 KEY: word problem,problem solving,linear inequality,graphing MSC: NAEP A3a, CAT5.LV19.50, IT.LV15.DI, S9.TSK1.PRA, S10.TSK1.PRA, TV.LV19.16, TV.LVALG.54

21. ANS: C DIF: L1 REF: 7-6 Systems of Linear InequalitiesOBJ: 7-6.1 Solving Systems of Linear Inequalities by Graphing STO: CA 9.0TOP: 7-6 Example 1 KEY: linear inequality, graphing,system of linear inequalities,graphing a system of linear inequalities MSC: NAEP A4g, S9.TSK1.PRA, S10.TSK1.PRA, TV.LV19.16, TV.LV19.52, TV.LVALG.54

22. ANS: B DIF: L1 REF: 7-6 Systems of Linear InequalitiesOBJ: 7-6.1 Solving Systems of Linear Inequalities by Graphing STO: CA 9.0TOP: 7-6 Example 1 KEY: linear inequality, graphing,system of linear inequalities,graphing a system of linear inequalities MSC: NAEP A4g, S9.TSK1.PRA, S10.TSK1.PRA, TV.LV19.16, TV.LV19.52, TV.LVALG.54

ID: A

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23. ANS: C DIF: L1 REF: 7-6 Systems of Linear InequalitiesOBJ: 7-6.1 Solving Systems of Linear Inequalities by Graphing STO: CA 9.0TOP: 7-6 Example 2 KEY: linear inequality, graphing,system of linear inequalities,graphing a system of linear inequalities MSC: NAEP A4g, S9.TSK1.PRA, S10.TSK1.PRA, TV.LV19.16, TV.LV19.52, TV.LVALG.54

SHORT ANSWER

24. ANS:

DIF: L1 REF: 7-6 Systems of Linear Inequalities OBJ: 7-6.1 Solving Systems of Linear Inequalities by Graphing STO: CA 9.0TOP: 7-6 Example 1 KEY: linear inequality,graphing,system of linear inequalities,graphing a system of linear inequalitiesMSC: NAEP A4g, S9.TSK1.PRA, S10.TSK1.PRA, TV.LV19.16, TV.LV19.52, TV.LVALG.54

25. ANS: admission fee: $3.25skate rental fee: $2.50

DIF: L2 REF: 7-4 Applications of Linear Systems OBJ: 7-4.1 Writing Systems of Linear Equations STO: CA 9.0KEY: word problem,problem solving,system of linear equations,graphing a system of linear equations,substitution method,elimination method MSC: NAEP A4g, CAT5.LV19.54, IT.LV15.AM, S9.TSK1.PRA, S10.TSK1.PRA, TV.LV19.16, TV.LV19.17, TV.LV19.18, TV.LV19.52, TV.LVALG.54