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Alg 1 review for test chap 7 Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. Tom has a collection of 30 CDs and Nita has a collection of 12 CDs. Tom is adding 2 CDs a month to his collection while Nita is adding 4 CDs a month to her collection. Write and graph a system to find the number of months after which they will have the same number of CDs. Let x represent the number of months and y the number of CDs. a. c. y y 50 50 (9, 48) 45 45 40 35 Number of CDs Number of CDs 40 30 25 20 15 35 30 25 15 10 10 5 5 0 0 1 2 3 4 5 6 7 8 9 10 (3, 24) 20 0 x 0 1 2 Number of Months 9 months 4 5 6 7 8 9 10 x 3 months b. d. y 50 50 45 45 40 40 35 Number of CDs Number of CDs y (3, 35) 30 25 20 15 30 25 20 15 10 5 5 0 1 2 3 4 5 6 7 8 9 10 x (9, 48) 35 10 0 0 0 1 Number of Months 3 months ____ 3 Number of Months 2 3 4 5 6 7 8 9 10 x Number of Months 48 months 2. Find a solution to the following system of equations. Use either elimination or substitution methods. a. (2, 16) b. (62, 16) c. (0, 1) d. (–2, 0) ____ 3. Which graph represents the following system of equations? y = 3x + 2 y = –x – 1 y a. c. –4 –2 4 4 2 2 O ____ 2 4 x –2 O –2 –4 –4 y –2 –4 –2 b. –4 y 4 2 2 2 4 x 4 x 2 4 x y d. 4 O 2 –4 –2 O –2 –2 –4 –4 4. What is the solution of the system of equations? Substitution method is easiest in this case. y = –3x + 6 y = –2x – 1 a. (7, –15) b. (–5, 9) c. (–1.4, 10.2) d. (–15, 7) Graph this system if necessary. Tell whether the system has no solution, one solution, or infinitely many solutions. ____ 5. y = –4x – 3 y = –4x + 2 a. no solutions b. one solution c. infinitely many solutions Solve the system of equations using substitution. ____ 6. y = 2x + 1 y = 3x + 4 a. (7, 3) ____ ____ 7. y = 4x – 8 y = 2x – 10 a. (5, 13) b. (3, 13) c. (3, 7) d. (–3, –5) b. (3, 4) c. (3, –4) d. (–1, –12) 8. The sum of two numbers is 68. Their difference is 28. Write a system of equations that describes this situation. Solve by elimination to find the two numbers. a. x + y = 68 c. x + y = 28 x – y = 28 y – x = 68 43 and 15 43 and 21 b. x + y = 68 d. x – y = 68 x – y = 28 x + y = 28 48 and 20 47 and 21 Solve the system using elimination. ____ 9. 5x + y = 13 4x – y = 5 a. (1, 4) ____ 10. 4x + 2y = 6 2x + 6y = 28 a. (–1, 5) b. (3, 2) c. (2, 3) d. (3, –2) b. (5, –1) c. (–1, 3) d. (2, 4) ____ 11. 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 number of nickels and dimes that are in the jar. a. 30 nickels and 30 dimes c. 29 nickels and 31 dimes b. 31 nickels and 29 dimes d. 28 nickels and 32 dimes ____ 12. By what number should you multiply the first equation to solve using elimination? 3x – 2y = –9 12x + 3y = –3 a. 4 b. 6 c. 3 d. 12 Graph the inequality. ____ 13. y a. –4 –2 y c. 4 4 2 2 O 2 4 x –4 –2 O –2 –2 –4 –4 2 4 x y b. –4 ____ 14. –2 4 4 2 2 O 2 4 x –4 –2 O –2 –2 –4 –4 2 4 x 2 4 x 2 4 x You need to rearrange the inequality before graphing it. y y c. a. –4 –2 4 4 2 2 O 2 4 x –2 –2 O –2 –4 –4 y –4 –4 –2 b. ____ 15. y d. y d. 4 4 2 2 O 2 4 x –4 –2 O –2 –2 –4 –4 y a. –4 –2 4 4 2 2 O 2 4 x –2 O –2 –4 –4 y –2 –4 –2 b. –4 y c. 4 2 2 2 4 x 4 x 2 4 x 2 4 x y d. 4 O 2 –4 –2 O –2 –2 –4 –4 ____ 16. y a. –4 –2 y c. 4 4 2 2 O 2 4 x –4 –2 O –2 –2 –4 –4 y b. –4 4 4 2 2 O –2 y d. 2 x 4 –4 –2 O –2 –2 –4 –4 2 Write the linear inequality shown in the graph. ____ 17. y 4 2 –4 –2 O 2 4 x –2 –4 a. b. ____ 18. c. d. c. d. y 4 2 –4 –2 O 2 4 x –2 –4 a. b. 4 x ____ 19. Find a solution of the linear inequality. You do not need to graph this equation to find the answer. a. (3, 4) b. (2, 1) c. (3, 0) d. (1, 1) Solve the system of linear inequalities by graphing. The overlap of the shaded regions is shown in each graph. ____ 20. y a. –4 4 4 2 2 O –2 2 4 x –4 O –2 –2 –2 –4 –4 y b. –4 y c. 4 2 2 O 2 4 x 4 x 2 4 x y d. 4 –2 2 –4 O –2 –2 –2 –4 –4 Short Answer 21. Graph the following linear inequalities on the same coordinate plane. What figure does the solution to all three inequalities make? Alg 1 review for test chap 7 Answer Section MULTIPLE CHOICE 1. ANS: A PTS: 1 DIF: L2 REF: 7-1 Solving Systems By Graphing OBJ: 7-1.1 Solving Systems By Graphing NAT: NAEP 2005 A4d | NAEP 2005 A4g | ADP J.3.3 | ADP J.4.3 | ADP J.5.2 STA: CO 9.2.3.b | CO 9.2.5.a TOP: 7-1 Example 2 KEY: word problem | problem solving | system of linear equations | graphing a system of linear equations 2. ANS: D PTS: 1 DIF: L3 REF: 7-1 Solving Systems By Graphing OBJ: 7-1.1 Solving Systems By Graphing NAT: NAEP 2005 A4d | NAEP 2005 A4g | ADP J.3.3 | ADP J.4.3 | ADP J.5.2 STA: CO 9.2.3.b | CO 9.2.5.a TOP: 7-1 Example 1 KEY: system of linear equations | graphing a system of linear equations 3. ANS: D PTS: 1 DIF: L2 REF: 7-1 Solving Systems By Graphing OBJ: 7-1.1 Solving Systems By Graphing NAT: NAEP 2005 A4d | NAEP 2005 A4g | ADP J.3.3 | ADP J.4.3 | ADP J.5.2 STA: CO 9.2.3.b | CO 9.2.5.a TOP: 7-1 Example 1 KEY: system of linear equations | graphing a system of linear equations 4. ANS: A PTS: 1 DIF: L2 REF: 7-1 Solving Systems By Graphing OBJ: 7-1.1 Solving Systems By Graphing NAT: NAEP 2005 A4d | NAEP 2005 A4g | ADP J.3.3 | ADP J.4.3 | ADP J.5.2 STA: CO 9.2.3.b | CO 9.2.5.a TOP: 7-1 Example 1 KEY: system of linear equations | graphing a system of linear equations 5. ANS: A PTS: 1 DIF: L2 REF: 7-1 Solving Systems By Graphing OBJ: 7-1.2 Analyzing Special Types of Systems NAT: NAEP 2005 A4d | NAEP 2005 A4g | ADP J.3.3 | ADP J.4.3 | ADP J.5.2 STA: CO 9.2.3.b | CO 9.2.5.a TOP: 7-1 Example 4 | 7-1 Example 5 KEY: system of linear equations | graphing a system of linear equations | no solution | infinitely many solutions 6. ANS: D PTS: 1 DIF: L2 REF: 7-2 Solving Systems Using Substitution OBJ: 7-2.1 Using Substitution NAT: NAEP 2005 A4g | ADP J.3.3 | ADP J.5.2 STA: CO 9.2.3.b TOP: 7-2 Example 1 KEY: system of linear equations | substitution method 7. ANS: D PTS: 1 DIF: L2 REF: 7-2 Solving Systems Using Substitution OBJ: 7-2.1 Using Substitution NAT: NAEP 2005 A4g | ADP J.3.3 | ADP J.5.2 STA: CO 9.2.3.b TOP: 7-2 Example 1 KEY: system of linear equations | substitution method 8. ANS: B PTS: 1 DIF: L3 REF: 7-3 Solving Systems Using Elimination OBJ: 7-3.1 Adding or Subtracting to Solve Systems NAT: NAEP 2005 A4g | ADP J.3.3 | ADP J.5.2 STA: CO 9.2.3.b KEY: word problem | problem solving | system of linear equations | elimination method | adding or subtracting equations 9. ANS: C PTS: 1 DIF: L2 REF: 7-3 Solving Systems Using Elimination OBJ: 7-3.1 Adding or Subtracting to Solve Systems NAT: NAEP 2005 A4g | ADP J.3.3 | ADP J.5.2 STA: CO 9.2.3.b 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. TOP: 7-3 Example 1 KEY: system of linear equations | elimination method | adding or subtracting equations ANS: A PTS: 1 DIF: L2 REF: 7-3 Solving Systems Using Elimination OBJ: 7-3.2 Multiplying First to Solve Systems NAT: NAEP 2005 A4g | ADP J.3.3 | ADP J.5.2 STA: CO 9.2.3.b TOP: 7-3 Example 3 KEY: system of linear equations | elimination method | adding or subtracting equations ANS: B PTS: 1 DIF: L2 REF: 7-3 Solving Systems Using Elimination OBJ: 7-3.2 Multiplying First to Solve Systems NAT: NAEP 2005 A4g | ADP J.3.3 | ADP J.5.2 STA: CO 9.2.3.b TOP: 7-3 Example 4 KEY: word problem | problem solving | system of linear equations | elimination method | adding or subtracting equations ANS: A PTS: 1 DIF: L2 REF: 7-3 Solving Systems Using Elimination OBJ: 7-3.2 Multiplying First to Solve Systems NAT: NAEP 2005 A4g | ADP J.3.3 | ADP J.5.2 STA: CO 9.2.3.b TOP: 7-3 Example 3 KEY: system of linear equations | elimination method | adding or subtracting equations ANS: B PTS: 1 DIF: L2 REF: 7-5 Linear Inequalities OBJ: 7-5.1 Graphing Linear Inequalities NAT: NAEP 2005 A3a | ADP J.4.4 STA: CO 9.2.5.a TOP: 7-5 Example 1 KEY: linear inequality | graphing ANS: A PTS: 1 DIF: L3 REF: 7-5 Linear Inequalities OBJ: 7-5.1 Graphing Linear Inequalities NAT: NAEP 2005 A3a | ADP J.4.4 STA: CO 9.2.5.a TOP: 7-5 Example 2 KEY: linear inequality | graphing ANS: C PTS: 1 DIF: L2 REF: 7-5 Linear Inequalities OBJ: 7-5.1 Graphing Linear Inequalities NAT: NAEP 2005 A3a | ADP J.4.4 STA: CO 9.2.5.a TOP: 7-5 Example 1 KEY: linear inequality | graphing ANS: B PTS: 1 DIF: L2 REF: 7-5 Linear Inequalities OBJ: 7-5.1 Graphing Linear Inequalities NAT: NAEP 2005 A3a | ADP J.4.4 STA: CO 9.2.5.a TOP: 7-5 Example 1 KEY: linear inequality | graphing ANS: D PTS: 1 DIF: L2 REF: 7-5 Linear Inequalities OBJ: 7-5.1 Graphing Linear Inequalities NAT: NAEP 2005 A3a | ADP J.4.4 STA: CO 9.2.5.a TOP: 7-5 Example 1 KEY: linear inequality | graphing ANS: A PTS: 1 DIF: L2 REF: 7-5 Linear Inequalities OBJ: 7-5.1 Graphing Linear Inequalities NAT: NAEP 2005 A3a | ADP J.4.4 STA: CO 9.2.5.a TOP: 7-5 Example 1 KEY: linear inequality | graphing ANS: D PTS: 1 DIF: L2 REF: 7-5 Linear Inequalities OBJ: 7-5.1 Graphing Linear Inequalities NAT: NAEP 2005 A3a | ADP J.4.4 STA: CO 9.2.5.a TOP: 7-5 Example 1 KEY: linear inequality | graphing ANS: B PTS: 1 DIF: L2 REF: 7-6 Systems of Linear Inequalities OBJ: 7-6.1 Solving Systems of Linear Inequalities by Graphing NAT: NAEP 2005 A4g | ADP J.4.4 STA: CO 9.2.5.a TOP: 7-6 Example 1 KEY: linear inequality | graphing | system of linear inequalities | graphing a system of linear inequalities SHORT ANSWER 21. ANS: y 6 4 2 –4 –2 O 2 4 x –2 –4 –6 The figure is an isosceles triangle. PTS: 1 DIF: L4 REF: 7-5 Linear Inequalities OBJ: 7-5.1 Graphing Linear Inequalities NAT: NAEP 2005 A3a | ADP J.4.4 STA: CO 9.2.5.a KEY: linear inequality | graphing