Oregon Focus on Linear Equations Lesson 1 Answers

Transcription

1 Lesson 1 Answers 1. a. Nathan; multiplication b. Subtraction a b. $ a. ( ) 4 or b. $ Answers may vary. 20. Answers may vary. 21. ( ) 4 = (4 2) 5 = (2 + 2) = 1 1

2 Lesson 2 Answers x 6x 4 Value 2 6( 2) (0) ( 1 2 ) (3) (8) True 18. False 19. False 20. True 21. True 22. False 23. False 24. False 25. a. 18 units b. 26 units c. 22 units 26. a. 10 square units b. 30 square units c. 18 square units 27. a. 12x + 16y b. $116 c. Answers may vary. 28. a. $33 b. $48 c. Answers may vary x x 3 2 5( 3) 3 2 Value 9 5(0) (4) ( 1 1 )

3 Lesson 3 Answers 1. 5x x m x h x , , a. 7( ) b. $ x x x x + y 16. 4x + 7y y + 7x x x x 21. 5x x x x x x x A. and B. 10x A. and C. 3x No. Answers may vary. 31. a. 50 = c. 53 d. 32 b a x b. $92 3

4 Lesson 4 Answers 1. x = x = x = 9 4. x = x = x = x = x = 6 9. x = a. Incorrect; x = 42 b. Correct c. Incorrect; x = 7 d. Incorrect; x = See student work; x = x = 48; x = x + ( 53) = 89; x = x ( 7) = 7; x = x 16 = 102; x = x = ; x = x = 6; x = x = 12; x = 7 x 19 = 12; x = a. 7x b. 7x = 84; x = x = x = x = x = 7 4 or x = x = x x m x a. 5 b. 24 c. 6 d. 3 e. 9 f. 100 g. 7 h. 6 4

5 Lesson 5 Answers 1. x = 4 2. x = x = x = x = x = x = x = 5 9. x = a F b C 11. a. subtracted instead of adding 6, x = 11 b. subtracted from wrong side of equation, x = 3 c. divided by 8 instead of multiplying, x = x + 7 = 25; x = x 3 6= 1; x = x = 72; x = x + 4 = 3; x = a. $40 b m = S c. m = hours 18. a. the amount of Ryan s commission b. $138 c. $47, = = = = x x x 26. 5x x

6 Lesson 6 Answers 1. See student work; subtract x from both sides, then subtract 1 from both sides, then divide both sides by 2; x = 4 2. x = 5 3. x = x = 1 5. x = 1 6. x = 0 7. x = Answers may vary. 9. a x = 0.75x b. x = 24 c. $ x = x = x = x = x = x = x = x = x = He forgot to distribute the 3 and the 7. x = a. Movies Rented Total Cost Option A Total Cost Option B 0 $40 $0 1 $41 $6 2 $42 $12 3 $43 $18 4 $44 $24 5 $45 $30 6 $46 $36 7 $47 $42 8 $48 $48 9 $49 $54 b x c. 6x d x = 6x; x = 8 e. After 8 movie rentals the cost is the same. f. Option A. His total cost would only be $55 as opposed to $90 under Option B. 21. True 22. False 23. False 24. True 6

7 Lesson 7 Answers 1. y axis II I origin x axis 9. a. Test Score III IV Missing Assignments b. Grade appears to go down as the number of missing assignments goes up a. Answers may vary. b. No. Scatter plot shows no relationship. 11. a. Heart rate 3. F = ( 4, 0) G = (7, 3) H = (0, 0) I = (2, 8) J = (0, 5) K = ( 9, 4) 4. Quadrant IV 5. y-axis 6. Quadrant I 7. x-axis 8. Quadrant III 12. x = x = x = x = 11 Minutes run b. goes up quickly, then levels off c. answers may vary; around x = 9 2 or x = x = x = 2 7

8 Block 1 Review Answers 17. x 3x+ 2 4 Output x = 9 2 or x 5x + 1 Output 2 5( 2) (0) ( 1 2 ) or (3) (7) x x ( 3) or (0) (4) or ( 1 0 ) x x x x x x x x x x x + 10x + 6x = 24x 31. 5(x 4) = 5x x = 22 8

9 Block 1 Review Answers 33. x = x = x = x = x = x + 7 = 73; x = x 10 = 66; x = = x 3 ; x = x = x = x = x = x = x = x = x = a. 3x b x c. 3x = x; x = 10; Somebody would need to bowl 10 games. d. Option B. It will be cheaper. 55. a x b x c x = x; x = (0, 4) 57. ( 1, 4) 58. (3, 0) 59. ( 3, 1) Answers may vary. 64. a. 47. a. $72 b m = S c. m = x = 4 Number of people 49. x = x = x = 11 Temperature b. Yes. As the temperature goes up, more people are at the park. c. Answers may vary. 9

10 Lesson 8 Answers 1. 3, 5, 7, 9, 11, 13; SV: 3 Op: , 150, 175, 200, 225, 250 SV: 125 Op: , 22, 17, 12, 7, 2 SV: 27 Op: , 1, 5, 9, 13, 17 SV: 3 Op: , 34, 45, 56, 67, 78 SV: 23 Op: SV: 8 Op: +8; SV: 10.5 Op: 1.1; SV: 9 Op: 4; SV: 1 3 Op: ; a. b. 4 cm c. 12 cm; 20 cm d. SV: 4 Op: +8 e. 52 cm , 5, 5 1 2, 6, 6 1 2, 7 SV: Op: , 2.7, 3.1, 3.5, 3.9, 4.3 SV: 2.3 Op: , 22, 2, 18, 38, 58 SV: 42 Op: a. Minutes Spent Downhill Skiing Total Daily Calories Burned 0 1, b. 6 c. Minutes Spent Downhill Skiing d. 1,470 calories Total Daily Calories Burned 0 1, , , , , a. SV: 4.5 Op: 0.3 b. 4.5, 4.2, 3.9, 3.6, 3.3 c. The 10 th day d. Day See student work. 18. x 6x + 7 Value 2 6( 2) (0) ( 1 2 ) (5) (10) x 3(x 1) Value 3 3( 3 1) (0 1) (2.2 1) (8 1) (21 1) a. 4 cm b. 6 cm; 8 cm c. 10 cm; 12 cm d. SV: 4 Op: +2 e. 30 cm 10

11 Lesson 9 Answers 1. SV: 10, Op: 2 x y SV: 4, Op: +1 x y SV: 2, Op: +0.5 x y SV: 9, Op: 3 x y SV: 3 Op: None x y SV: 20 Op: 5 x y a. 10. Time (seconds), x Feet off the Ground, y b. SV: 60 Op: 10 c. how tall the slide is d. 6 seconds Answers may vary. See student work (2x 3) = 12x (x + 7) = 5x ( 3x + 26) = 3x (x + 10) = 40x SV: 1 Op: +2 x y SV: 4 Op: 1 3 x y

12 Lesson 10 Answers 1. Answers may vary. 2. Answers may vary. 3. Answers may vary. 4. a. SV: 82 Op: +26 b. Number of Tickets c. Amount of bill ($$) Monthly Cost of Insurance # of speeding tickets d. $394 per month 5. a. SV: 799 Op: 70 b. Years Passed Value of Maggie s Laptop 0 $799 1 $729 2 $659 3 $589 4 $519 5 $ a. SV: 200 Op: 14 b. Weeks Passed c. Amount owed ($) Amount Owed Parents 0 $200 1 $186 2 $172 3 $158 4 $144 5 $130 Weeks passed d. 15 weeks; The last payment was $4. 7. a. SV: 61 Op: +7 b. Minutes Elevation Hiking c. Elevation c. Value of the laptop Minutes d. Approximately 9 minutes d. 12 years Years passed 12

13 Lesson 10 Answers 8. a. Victor s SV: 3 Op: Mike s SV: 1 Op: b. Minutes Passed Victor s Pieces Eaten _ _ _ _ Minutes Passed Mike s Pieces Eaten _ _ _ _ _ _ c. It was a tie. 9. a. SV: $1,000 Op: +$250 b. $5,500 c. $7, , 11, 8, 5, 2, 1; SV = 14 Op = , 4.6, 3.4, 2.2, 1, 0.2; SV = 5.8 Op = , 15, 21, 27, 33, 39; SV = 9 Op = , 1, 1 2 3, 2 1 3, 3, ; SV = 1 3 Op = x = x = x = x = x = x =

14 Lesson 11 Answers bugs per day dollars per day per rose steps per minute 5. ROC: +4; SV: 5 6. ROC: 3; SV: 6 7. ROC: +1; SV: 3 8. ROC: +2; SV: 0 9. ROC: 2; SV: ROC: ; SV: x y x y x y a. $0.40 per mile b. $16.00 c. $ a. 12 ants b. 30 ants c. 282 ants 16. a. Minutes Traveled Distance to Work There! b. ROC: 0.5 miles per minute c. Yes. 9 minutes 24 seconds 17. Answers may vary. 18. Answers may vary. 19. Answers may vary. 14

15 Lesson 12 Answers 1. y = 6 + 8x 2. y = x 3. y = 7.1x 4. y = 7 3x 5. y = y = x 7. y-int = 4; ROC = +8; y = 4 + 8x 8. y-int = 12; ROC = 1; y = 12 x 9. y-int = 6; ROC = +2; y = 6 + 2x 10. y-int = 31; ROC = +1.5; y = x 11. y-int = 7; ROC = +4; y = 7 + 4x 12. y-int = 1; ROC = ; y = x 13. a. 2 problems per minute b. 12 c. y = x d. minutes e. problems finished 14. a. y = 6x b. $ a. 65 b. 0 c. y = a. 32 b. 8 feet per second c. y = 32 8x 17. y-int = 1; ROC = +3; y = 1 + 3x x y y-int = 23.5; ROC = 0.5; y = x x y y-int = 14; ROC = +11; y = x x y x 0.5x 1 Value 1 0.5( 1) (0) (1) (2) (4) x 2x + 7 Value 2 2( 2) ( 1) (0) (3) (5) dollars per hour per hour words per minute points per assignment 15

16 Oregon Focus on Equations Lesson 13 Answers 1. y-int = 8; ROC = y-int = 11; ROC = x y x days y earnings 6 $ $ $1, $1, $1, y-int = 4; ROC = y-int = 5; ROC = 4 5. y-int = 0; ROC = y-int = 1; ROC = x y x = x = x = x = 4 or y-int = 8; ROC = y-int = 6; ROC = 0 9. y-int = 2; ROC = a. x y x = x = x = x 2x 3 y 0 2(0) 3 3 b. 26. x = (3) (9) (10) (13) 3 23 Height in inches 27. x = x x + 9 y x x y ( 7) ( 3) (1) (4) (15) x y a. x seconds Week y meters run b. 59 seconds; Answers may vary. c. 3,600 seconds d. 24,480 meters e miles f. Not reasonable. One could not sprint that far. 16

17 Lesson 14 Answers 1. m = 3 2. m = See student work. 16. See student work. 17. Answers may vary. 3. m = undefined 4. m = m = Answers may vary. 6. m = negative 8. positive 19. Answers may vary. 9. zero 10. negative 11. positive 12. undefined 13. a feet feet 22. Yes. See student work b Undefined c. They are the same. Yes. Same as both See student work. 17

18 Lesson 15 Answers Undefined a. ROC; a. 4 5 b. Slope Formula; 4 3 c. Slope Triangle; 5 2 b. 0.8 c. x y d. Six. Limitless. 12. a. (4, 94) and (9, 204) b. slope = 22 c. Cost per month of the gym membership or a. minutes it is the counter b. 120 feet per minute; Answers may vary. c. 1,800 feet 15. a. 1 3 b. Amount of pop draining out of bottle per hour c. 6 hours 16. E 17. F 18. A 19. B 20. D 21. G 22. C 18

19 Block 2 Review Answers 10. a. 1. 8, 1, 6, 13, 20, 27 ; SV: 8; Op: , 110, 128, 146, 164, 182; SV: 92; Op: +18 b. 3. 7, 7.6, 8.2, 8.8, 9.4, 10; SV: 7; Op: , 16, 19, 22, 25, 28; SV: 13; Op: SV: 18 Op: 13 9 th term: SV: a. 6 Op: b. 10, 14 c. SV: 6 Op: +4 d. 30 units 9 th term: SV: 12 Op: 3 x y a. Answers may vary. b. Answers may vary. 12. a. SV: 150 Op: +12 b. x y c SV: 2 Op: x y d. 13 weeks; $6 19

20 Block 2 Review Answers 13. a. SV: 3.35 Op: b. x y c ROC = +3.5; y-int = 9.9; y = x 26. ROC = +4; y-int = 7; y = 7 + 4x 27. a. $42 b. $3.10 c. y = x Price in $ 28. ROC = +5; y-int = ROC = 6; y-int = 7 d. 17 years Year coins per day miles per hour 16. $0.38 per doughnut 17. SV: 2 ROC: SV: 33 ROC: SV: 13 ROC: a. 2 lbs b. 163 lbs c. 129 lbs d. No. Answers may vary. 21. y = 2 + 6x 22. y = x 23. y = x 24. ROC = 6; y-int = 39; y = 39 6x 30. ROC = ; y-int = ROC = 2; y-int = ROC = 2 9 ; y-int = ROC = 0; y-int = x y x y x y

21 Block 2 Review Answers 37. See student work; m = See student work; m = See student work; m = Answers may vary feet 44. a. 1 b. less steep; 1 < undefined 41. Answers may vary a. Rate of change; slope = 2 b. Slope formula; slope = 5 4 c. Slope triangle; slope = Answers may vary. 52. a. (3, 510) and (5, 800) b. slope = 145 c. cost per night 21

22 Lesson 16 Answers a. Taylor did run over rise, not rise over run. b. Taylor graphed y = 3, not x = a. x y 2 1 b c. Answers may vary

23 Lesson 16 Answers 12. They all have the same slope but different y-intercepts. 13. a. Answers may vary b. Answers may vary c. Answers may vary d. Answers may vary 14. a. Answers may vary. 15. a. x y b c. (0, 3) d. y = 2.5x + 3 e. 28 inches 16. a. y = 2x + 3 b. No c. 17. C b. Answers may vary. 18. A 19. B c. Answers may vary. 21. undefined zero d. Answers may vary

24 Lesson 17 Answers 1. m = 3 4, b = 3, y = 3 4 x m = 5 2, b = 5, y = 5 2 x m = 1, b = 3, y = x 3 4. m = 0, b = 2, y = 2 5. m = 2 3, b = 0, y = 2 3 x 6. m = undefined, b = none, x = 3 7. a. y = 6x + 20 b. $128 c. 32 months 8. a. y = 1 2 x + 12 b. $72 c. 53 miles 9. a. y = 3x + 5 b. 29 inches c. 14 weeks 10. a. y = 3 2 x + 20 b. 5 gallons c minutes 11. a. m y = 1 3 x + 2 n y = 1 3 x p y = 1 3 x 4 b. Same slope c. Parallel 12. a. 14 b. 12 c False 14. True 15. True 16. False 17. True 18. False 24

25 Lesson 18 Answers 1. y = 6 5 x y = 4x y = x y = 3 5. a. y = 50,000x + 3,400,000 b. 4,400,000 people 6. y = 2x 6 7. y = 3 4 x y = x y = 5 2 x y = 1 2 x y = a. m = 0.10 and (14, 5.40) b. y = 0.1x + 4 c. $ a. (2, 9) and (8, 12) 30. y = 30x + 45 b. y = 1 2 x + 8 c. 18 pounds; 31. y = 0.3x + 3 Answers may vary AB : y = 2x 15 y = 1 4 x + 6 BC : y = 9 4 x + 14 CD : y = 1 4 x 2 AD : y = 9 4 x 2 Line AB and CD have the same slope. Line BC and AD have the same slope. 23. a. (6, 32) and (11, 47) b. y = 3x + 14 c. $14 d. Cost per hour e. $ y = 2x y = 1 3 x x = y = 3x y = x y = 1 3 x y = 1 2 x 17. y = 4 5 x y = x y = x = 1 25

26 Lesson 19 Answers 1. C 2. B 3. E 4. A 5. F 6. D 7. y = 4x y = 3x y = 1 3 x y = 2 5 x y = 1 2 x y = 2x y = 3 4 x y = 7x y = 4x x + 3y = y = 1 3 (x 9) y = 2 5 x y = 3x y = 5x 21. y = 1 2 x y = x y = x = y = 3x 26

27 Lesson 20 Answers 1. y = 2 5 x 4 2. y = 3x y = 1 2 x y = 1 4 x y = 4 3 x 2 6. y = 2x x = 2 8. y = 3 4 x 3 9. y = 3x 10. y = 5 2 x y = x y = Answers may vary. 14. a. y = 0.1x + 9 or y = 1 10 x + 9 b. $9 c. $0.10 per minute d. $ Yes 16. No 17. Yes 18. Yes 19. No 20. No 21. No. She should have been charged $ y = 1 2 x x + y = y = x y = 2x y = 2x y = y = x y = 2x 30. y = 5x y = 2 5 x x = y = 1 3 x 1 27

28 Oregon Focus on Linear Equations Lesson 21 Answers 6. Linear y = x² + 2 x y 2 ( 2)² + 2 = y = 3 x x y 2 3 ( 2) = y = 2x 5 x 2 1 y 2( 2) 5 = Quadratic 5. Exponential 7. Non-linear; Exponential 8. Non-linear; Quadratic 9. Non-linear; Inverse Variation 10. Linear 11. Linear 12. Non-linear; Exponential bacteria meters 15. x = x = x = x = x = x =

29 Block 3 Review Answers Answers may vary. 8. m = 4; b = 2; y = 4x 2 9. m = 3 5 ; b = 1; y = 3 5 x m = 1; b = 4; y = x a. y = 2x + 7 b. 21 inches c. 11 weeks 12. y = 3 4 x y = 5x y = x y = 2 5 x 16. y = 2x y = 1 2 x y = x y = 5 2 x y = 2x y = 1 3 x y = 3x y = a. m = 20; (8, 225) b. y = 20x + 65 c. $405 29

30 Block 3 Review Answers 25. a. (4, 32) and (10, 56) b. y = 4x + 16 c. 16 d. Charge per hour e. $ y = 2x x = y = 1 3 x y = 1 2 x y = 1 4 x y = 4 5 x y = 1 3 x y = 2x 31. y = 3x y = 2x Yes 39. Yes 33. y = 3x No 41. Non-linear; Quadratic 42. Linear 34. y = 3 2 x Non-linear; Exponential 44. Non-linear; Quadratic 45. Linear 46. Non-linear; Inverse Variation 30

31 Lesson 22 Answers 14. AB CD and BC AD 1. Same; Infinite 2. Intersecting; One 3. Parallel; None 4. Intersecting 15. Their paths were the same. 16. Answers may vary. 17. Answers may vary. 5. Same 18. The equations should have different slopes. 19. No. She gave different slopes and similar y-intercepts. She needed to give similar slopes. 20. True 6. Parallel 21. False 22. False 23. True 7. Parallel; None 8. Intersecting; One 9. Intersecting; One 10. Intersecting; One 11. Same; Infinite 12. Intersecting; One 24. 8x x x 27. 4x x + 7y x + 2y 31

32 Lesson 23 Answers 1. a. Put both in slope-intercept form. b. Graph. c. Find the point of intersection. d. Substitute back in and check. 16. (1, 1) 17. No solution. Parallel lines. 18. a. y = 8x b. y = 12x c. 2. (4, 0) 3. ( 1, 3) 4. (3, 3) 5. No 6. Yes 7. Yes d. (5, 60); After 5 weeks they both have $ a. y = 2x + 2y = 42 b. y = 2x + 3 c. 8. a. No b. Yes 9. (4, 5) 10. (1, 1) 11. (6, 4) 12. Same line. Infinite solutions. 13. (3, 3) 14. ( 3, 5) 15. (6, 4) d. Length = 15 feet; Width = 6 feet 20. (10, 90) 21. Intersecting; One 22. Same; Infinite 23. Parallel; None 24. Parallel; None 25. Intersecting; One 26. Same; Infinite 32

33 Lesson 24 Answers 1. (1, 2) y = 3x 1 x y x y = 2x + 4 y ( 2, 4) y = x + 6 x y x y = 1 2 x + 5 y They were getting further apart. 4. (3, 9) 5. (1, 3) 11. a. y = 15x b. y = 35x c. Carlos Savings Account Balance Months, x Total Savings, y 0 $100 1 $115 2 $130 3 $145 4 $160 5 $175 6 $190 7 $205 8 $220 Ana s Savings Account Balance Months, x Total Savings, y 0 $400 1 $365 2 $330 3 $295 4 $260 5 $225 6 $190 7 $155 8 $120 d. After 6 months. They will both have $ a. (4, 1) 14. x = x = x = x = x = x = 2 6. (10, 34) 7. ( 4, 2) b. (2, 7) 8. ( 4, 11) 9. (0, 6) 10. a. (5, 27) b. See student work lawns 33

34 Lesson 25 Answers 1. x in #2 2. y in #1 3. y in #2 4. x in #1 5. Sometimes the intersection point is not an integer or it can be hard to see on the graph. 6. Graphing or substituting the solution back into the equations. 7. ( 1, 2) 8. (3, 2) 9. (6, 2) 10. (0, 4) 11. ( 7, 8) 12. (1, 1) 13. ( 1, 6) 14. ( 2, 7) 15. ( 3, 1) 16. a. x + y = 230 is the total number of single and doublescoop cones sold. 2x + 2.5y = 498 is the total amount of money brought in. b. x represents $2.00 cones y represents $2.50 cones c. (154, 76) d. Sold 154 single-scoop cones and 76 double-scoop cones. 17. a. x + y = 46; x y = 12 b. 29 and a. h + c = 340; c + 52 = h b. 196 horses 19. a. Tad: 6x + y = 67 Timothy: 4x + 3y = 54 b. (10.5, 4) c. $10.50 for a can of paint; $4.00 for a brush 20. parallel; none 21. intersecting; one 22. parallel; none 23. intersecting; one 24. same; infinite 25. parallel; none 34

35 Lesson 26 Answers 1. x; 0-step 2. x; 1-step; multiply the second equation by 2 3. y; 1-step; multiply the first or second equation by 1 4. y; 1-step; multiply the first equation by 4 5. y; 2-step; multiply the first equation by 3 and the second equation by 2 6. x; 1-step; multiply the second equation by 2 OR y and multiply the second equation by 7 7. She did not make it so the x or y coefficients were opposites. 8. (4, 7) 9. ( 2, 3) 10. ( 1, 0) 11. (5, 3) 13. (0, 1 2 ) 14. (6, 4) 15. ( 3 4, 1) 16. ( 3, 4) 17. a. 3x + y = 29 x + 2y = 18 b. One block is 8 and the other is a. x + y = 44 is the total number of candy bars sold x + 2y = 268 is the total amount of money brought in b. (20, 24) c. Twenty $1.00 bars and twenty-four $2.00 bars 19. (5, 2) 20. ( 1, 2) 21. (4, 0) 22. (7, 1) 23. (3, 1) 24. (7, 3) 12. ( 2, 5) 35

36 Lesson 27 Answers 1. Elimination. The x s are already opposites and in standard form. 2. Substitution. The x is already isolated. 3. Graphing. Both equations are in slope-intercept form. 4. Answers may vary. 5. Elimination; (4, 2) 6. Substitution; (2, 1) 7. Elimination; (3, 3) 8. Tables; (5, 6) 9. Substitution; (2, 4) 10. Graphing; ( 2, 2) 11. Elimination; ( 2, 6) 12. Graphing; (4, 1) 13. Substitution; (1, 2.5) 14. Same C and D; Intersecting A and F; Parallel B and E 36

37 1. x = weeks y = total savings Manny: y = 85x Susan: y = 100x + 95 Oregon Focus on Linear Equations Lesson 28 Answers 7. x = family A s total y = family B s total x + y = 1640 x = 2y (1154, 486) One family made $1,154 and one family made $ No 13. Yes 14. No 15. ( 6, 9) 2. x = price of a candy bar y = price of a soda Travis: 6x + 2y = 4.88 Beth: 2x + 3y = w = width of the garden l = length of the garden 2w + 2l = 184 w = x = miles driven y = total cost A: y = 0.1x + 8 B: y = 0.3x (40, 12) Both companies charge the same amount at 40 miles. 5. x = number of snaps y = total cost Old machine: y = 0.12x New machine: y = 0.09x (14000, 2780) The company would need to attach at least 14,000 snaps to make the new machine worthwhile. 6. x = calculators y = protractors Mrs. Wright: 40x + 30y = 485 Mr. Kinder: 20x +20y = 252 (10.7, 1.9) A calculator costs $10.70 and a protractor costs $ x = number of youths y = number of adults x + y = x + 8.5y = 3,907.5 (310, 250) 310 youth tickets were bought on Friday night. 9. x = price of a gallon of ice cream y = price of a container of strawberries Jeremiah: 3x + 4y = Gary: 5x + 2y = 22 (3.5, 2.25) A gallon of ice cream costs $3.50. A container of strawberries costs $ x = J-Series stereos y = K-Series stereos x + y = x + 92y = 3230 (11, 21) Eleven J-Series stereos sold and 21 K-Series stereos sold. 11. x = number of hours y = total miles traveled Nancy: y = 50x + 72 Pedro: y = 62x (6, 372) He will catch up with her after 6 hours. 16. (5, 0) 17. (6, 2) 18. Infinite solutions 19. (6, 3) 20. No solution 37

38 Block 4 Review Answers 1. Intersecting; One solution 2. Same; Infinite solutions 3. Parallel; No solutions 4. Intersecting; One solution 5. Parallel; No solutions 6. Same; Infinite solutions 7. Yes 8. No 9. Yes 10. (4, 1) 11. ( 2, 0) 12. ( 3, 1) 13. (6, 2) 14. (1, 1) y = 5x 4 x y ( 4, 9) y = 5 + x 16. (3, 5) x y y = 2x + 3 x y y = 3x + 3 x y ( 2, 9) 18. (4, 4) 19. a. y = x b. y = x c. Evan s Savings Account Balance Months, x Total Savings, y 0 $400 1 $380 2 $360 3 $340 4 $320 5 $300 6 $280 Lisa s Savings Account Balance Months, x Total Savings, y 0 $100 1 $140 2 $180 3 $220 4 $260 5 $300 6 $340 d. After 5 months they will both have $ (4, 3) 21. ( 3, 0) 22. (5, 2) 23. a. x + y = 79 represents the total number of Mr. James and Mr. Peters cows; x = 3y 5 represents 5 less than three times Mr. Peters amount b. (58, 21) Mr. James = 58 cows Mr. Peters = 21 cows 24. x; 0-step 38

39 Block 4 Review Answers 25. y; 1-step; multiply the first equation by x; 1-step; multiply the second equation by ( 1, 6) 28. (2, 3) 29. (1.5, 4) 30. a. x is the number of baseball caps and y is the number of t-shirts. Patrick bought one of each and paid $36 (x + y = 36). Sammy bought two hats and three t-shirts, paying $94 (2x + 3y = 94). b. x represents baseball caps y represents t-shirts c. (14, 22) Baseball cap = $14 T-shirt =$ Elimination; (4, 2) 32. Substitution; (3, 4) 33. Graphing; (3 4) 34. Elimination; (2, 1 4 ) 35. Substitution; ( 6, 0) 36. Substitution; ( 1, 7) 37. x = number of hours y = total cost of rental A - y = 2.5x + 8 B - y = x + 14 (4, 18) After 4 hours they are the same amount. Rentals are $18 for both companies after 4 hours. 38. x = youth tickets y = adult tickets x + y = x + 7y = 2,706 (185, 265) The theater sold 185 youth tickets and 265 adult tickets. 39. x = months passed y = total amount in savings account Jamal: y = 24x + 46 Emily: y = 15x (7, 214) After 7 months they will both have $214 in their accounts. 40. x = girl A s total y = girl B s total x + y = 28 x = 2y + 4 (20, 8) One girl made $20 while the other girl made $8. 39