Successfully reported this slideshow.
We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime.

AA Section 5-3

673 views

Published on

Solving Systems by Substitution

  • Be the first to comment

  • Be the first to like this

AA Section 5-3

  1. 1. 1. b 2. a 3. a. (6, 20); b. Plug into both equations 4. (2, 12) 5. (-8/3, -19,3) 6. b 7. It is a real world situation 8. a. Substitute to see answers are close; b. Substitute again 9. Advantage: Can see total number of solutions Disadvantage: Tough to find exact answer 10. a. 0; b. n/a; c. n/a 12. a. 1; b. (2, 4); c. Plug in 14. a. Graph; b. 3 solutions; c. (-3.8, .2), (-1, 3), (.8, 4.8) 16. Graph the two equations; they do not intercept 18. 20. Whole numbers ≥ 21 -1 0 1 2 3 4 5 2 T − 2π r 24. x = 11 or x = -11 22. h = 2π r
  2. 2. Section 5-3 Solving Systems by Substitution
  3. 3. Warm-up 1. Solve 8x + 8(5-2x) = -40 2. Evaluate 3x - 2 when x = 4y + 1
  4. 4. Warm-up 1. Solve 8x + 8(5-2x) = -40 8x + 8(5-2x) = -40 2. Evaluate 3x - 2 when x = 4y + 1
  5. 5. Warm-up 1. Solve 8x + 8(5-2x) = -40 8x + 8(5-2x) = -40 8x + 40 -16x = -40 2. Evaluate 3x - 2 when x = 4y + 1
  6. 6. Warm-up 1. Solve 8x + 8(5-2x) = -40 8x + 8(5-2x) = -40 8x + 40 -16x = -40 -8x + 40 = -40 2. Evaluate 3x - 2 when x = 4y + 1
  7. 7. Warm-up 1. Solve 8x + 8(5-2x) = -40 8x + 8(5-2x) = -40 8x + 40 -16x = -40 -8x + 40 = -40 -8x = -80 2. Evaluate 3x - 2 when x = 4y + 1
  8. 8. Warm-up 1. Solve 8x + 8(5-2x) = -40 8x + 8(5-2x) = -40 8x + 40 -16x = -40 -8x + 40 = -40 -8x = -80 x = 10 2. Evaluate 3x - 2 when x = 4y + 1
  9. 9. Warm-up 1. Solve 8x + 8(5-2x) = -40 8x + 8(5-2x) = -40 8x + 40 -16x = -40 -8x + 40 = -40 -8x = -80 x = 10 2. Evaluate 3x - 2 when x = 4y + 1 3(4y + 1) - 2
  10. 10. Warm-up 1. Solve 8x + 8(5-2x) = -40 8x + 8(5-2x) = -40 8x + 40 -16x = -40 -8x + 40 = -40 -8x = -80 x = 10 2. Evaluate 3x - 2 when x = 4y + 1 3(4y + 1) - 2 12y + 3 - 2
  11. 11. Warm-up 1. Solve 8x + 8(5-2x) = -40 8x + 8(5-2x) = -40 8x + 40 -16x = -40 -8x + 40 = -40 -8x = -80 x = 10 2. Evaluate 3x - 2 when x = 4y + 1 3(4y + 1) - 2 12y + 3 - 2 12y + 1
  12. 12. 1. Tables
  13. 13. 1. Tables Not very efficient
  14. 14. 1. Tables Not very efficient 2. Graphing by hand
  15. 15. 1. Tables Not very efficient 2. Graphing by hand Not very accurate
  16. 16. 1. Tables Not very efficient 2. Graphing by hand Not very accurate 3. Graphing Calculator
  17. 17. 1. Tables Not very efficient 2. Graphing by hand Not very accurate 3. Graphing Calculator Cheap way out
  18. 18. Example 1 Solve. x + y = 6  y = x + 2 
  19. 19. Example 1 Solve. x + y = 6  y = x + 2  x + (x + 2) = 6
  20. 20. Example 1 Solve. x + y = 6  y = x + 2  x + (x + 2) = 6 2x + 2 = 6
  21. 21. Example 1 Solve. x + y = 6  y = x + 2  x + (x + 2) = 6 2x + 2 = 6 2x = 4
  22. 22. Example 1 Solve. x + y = 6  y = x + 2  x + (x + 2) = 6 2x + 2 = 6 2x = 4 x=2
  23. 23. Example 1 Solve. x + y = 6  y = x + 2  x + (x + 2) = 6 y=x+2 2x + 2 = 6 2x = 4 x=2
  24. 24. Example 1 Solve. x + y = 6  y = x + 2  x + (x + 2) = 6 y=x+2 2x + 2 = 6 y=2+2 2x = 4 x=2
  25. 25. Example 1 Solve. x + y = 6  y = x + 2  x + (x + 2) = 6 y=x+2 2x + 2 = 6 y=2+2 2x = 4 y=4 x=2
  26. 26. Example 1 Solve. x + y = 6  y = x + 2  x + (x + 2) = 6 y=x+2 x+y=6 2x + 2 = 6 y=2+2 2x = 4 y=4 x=2
  27. 27. Example 1 Solve. x + y = 6  y = x + 2  x + (x + 2) = 6 y=x+2 x+y=6 2x + 2 = 6 y=2+2 2+4=6 2x = 4 y=4 x=2
  28. 28. Example 1 Solve. x + y = 6  y = x + 2  x + (x + 2) = 6 y=x+2 x+y=6 2x + 2 = 6 y=2+2 2+4=6 2x = 4 y=4 x=2 (2, 4)
  29. 29. Example 1 Solve. x + y = 6  y = x + 2  x + (x + 2) = 6 y=x+2 x+y=6 2x + 2 = 6 y=2+2 2+4=6 2x = 4 y=4 x=2 (2, 4) Always check your answer.
  30. 30. Example 1 Solve. x + y = 6  y = x + 2  x + (x + 2) = 6 y=x+2 x+y=6 2x + 2 = 6 y=2+2 2+4=6 2x = 4 y=4 x=2 (2, 4) Always check your answer. You’ll know you’re right.
  31. 31. Example 2 The Drama Club printed 1750 tickets for their spring play. They printed twice as many student tickets as adult tickets and half as many children’s tickets as adult tickets. Write a system of 3 equations and find the number of each ticket printed.
  32. 32. Example 2 The Drama Club printed 1750 tickets for their spring play. They printed twice as many student tickets as adult tickets and half as many children’s tickets as adult tickets. Write a system of 3 equations and find the number of each ticket printed. A = adult tickets S = student tickets C = children tickets
  33. 33. Example 2 The Drama Club printed 1750 tickets for their spring play. They printed twice as many student tickets as adult tickets and half as many children’s tickets as adult tickets. Write a system of 3 equations and find the number of each ticket printed. A = adult tickets S = student tickets C = children tickets     
  34. 34. Example 2 The Drama Club printed 1750 tickets for their spring play. They printed twice as many student tickets as adult tickets and half as many children’s tickets as adult tickets. Write a system of 3 equations and find the number of each ticket printed. A = adult tickets S = student tickets C = children tickets  A + S + C = 1750    
  35. 35. Example 2 The Drama Club printed 1750 tickets for their spring play. They printed twice as many student tickets as adult tickets and half as many children’s tickets as adult tickets. Write a system of 3 equations and find the number of each ticket printed. A = adult tickets S = student tickets C = children tickets  A + S + C = 1750   S = 2A  
  36. 36. Example 2 The Drama Club printed 1750 tickets for their spring play. They printed twice as many student tickets as adult tickets and half as many children’s tickets as adult tickets. Write a system of 3 equations and find the number of each ticket printed. A = adult tickets S = student tickets C = children tickets  A + S + C = 1750   S = 2A   C = 1/2 A
  37. 37. Example 2 The Drama Club printed 1750 tickets for their spring play. They printed twice as many student tickets as adult tickets and half as many children’s tickets as adult tickets. Write a system of 3 equations and find the number of each ticket printed. A = adult tickets S = student tickets C = children tickets  A + S + C = 1750 A + 2A + 1/2 A = 1750   S = 2A   C = 1/2 A
  38. 38. Example 2 The Drama Club printed 1750 tickets for their spring play. They printed twice as many student tickets as adult tickets and half as many children’s tickets as adult tickets. Write a system of 3 equations and find the number of each ticket printed. A = adult tickets S = student tickets C = children tickets  A + S + C = 1750 A + 2A + 1/2 A = 1750   S = 2A 7/2 A = 1750   C = 1/2 A
  39. 39. Example 2 The Drama Club printed 1750 tickets for their spring play. They printed twice as many student tickets as adult tickets and half as many children’s tickets as adult tickets. Write a system of 3 equations and find the number of each ticket printed. A = adult tickets S = student tickets C = children tickets  A + S + C = 1750 A + 2A + 1/2 A = 1750   S = 2A 7/2 A = 1750   C = 1/2 A A = 500
  40. 40. Example 2 The Drama Club printed 1750 tickets for their spring play. They printed twice as many student tickets as adult tickets and half as many children’s tickets as adult tickets. Write a system of 3 equations and find the number of each ticket printed. A = adult tickets S = student tickets C = children tickets  A + S + C = 1750 A + 2A + 1/2 A = 1750   S = 2A 7/2 A = 1750   C = 1/2 A A = 500 S = 1000
  41. 41. Example 2 The Drama Club printed 1750 tickets for their spring play. They printed twice as many student tickets as adult tickets and half as many children’s tickets as adult tickets. Write a system of 3 equations and find the number of each ticket printed. A = adult tickets S = student tickets C = children tickets  A + S + C = 1750 A + 2A + 1/2 A = 1750   S = 2A 7/2 A = 1750   C = 1/2 A A = 500 S = 1000 C = 250
  42. 42. Example 2 The Drama Club printed 1750 tickets for their spring play. They printed twice as many student tickets as adult tickets and half as many children’s tickets as adult tickets. Write a system of 3 equations and find the number of each ticket printed. A = adult tickets S = student tickets C = children tickets  A + S + C = 1750 A + 2A + 1/2 A = 1750   S = 2A 7/2 A = 1750   C = 1/2 A A = 500 S = 1000 They printed 500 adult tickets, 1000 student C = 250 tickets, and 250 children’s tickets
  43. 43. Example 3 Solve. y = 4x   xy = 36 
  44. 44. Example 3 Solve. y = 4x   xy = 36  x(4x) = 36
  45. 45. Example 3 Solve. y = 4x   xy = 36  x(4x) = 36 4x2 = 36
  46. 46. Example 3 Solve. y = 4x   xy = 36  x(4x) = 36 4x2 = 36 x2 = 9
  47. 47. Example 3 Solve. y = 4x   xy = 36  x(4x) = 36 4x2 = 36 x2 = 9 x2 = ± 9
  48. 48. Example 3 Solve. y = 4x   xy = 36  x(4x) = 36 4x2 = 36 x2 = 9 x2 = ± 9 x = 3 or x = -3
  49. 49. Example 3 Solve. y = 4x   xy = 36  x(4x) = 36 y = 4(3) 4x2 = 36 x2 = 9 x2 = ± 9 x = 3 or x = -3
  50. 50. Example 3 Solve. y = 4x   xy = 36  x(4x) = 36 y = 4(3) 4x2 = 36 y = 12 x2 = 9 x2 = ± 9 x = 3 or x = -3
  51. 51. Example 3 Solve. y = 4x   xy = 36  x(4x) = 36 y = 4(3) 4x2 = 36 y = 12 x2 = 9 y = 4(-3) x2 = ± 9 x = 3 or x = -3
  52. 52. Example 3 Solve. y = 4x   xy = 36  x(4x) = 36 y = 4(3) 4x2 = 36 y = 12 x2 = 9 y = 4(-3) x2 = ± 9 y = -12 x = 3 or x = -3
  53. 53. Example 3 Solve. y = 4x   xy = 36  x(4x) = 36 y = 4(3) Check: 4x2 = 36 y = 12 x2 = 9 y = 4(-3) x2 = ± 9 y = -12 x = 3 or x = -3
  54. 54. Example 3 Solve. y = 4x   xy = 36  x(4x) = 36 y = 4(3) Check: 4x2 = 36 y = 12 (3)(12) = 36 x2 = 9 y = 4(-3) x2 = ± 9 y = -12 x = 3 or x = -3
  55. 55. Example 3 Solve. y = 4x   xy = 36  x(4x) = 36 y = 4(3) Check: 4x2 = 36 y = 12 (3)(12) = 36 x2 = 9 y = 4(-3) (-3)(-12) = 36 x2 = ± 9 y = -12 x = 3 or x = -3
  56. 56. Example 3 Solve. y = 4x   xy = 36  x(4x) = 36 y = 4(3) Check: 4x2 = 36 y = 12 (3)(12) = 36 x2 = 9 y = 4(-3) (-3)(-12) = 36 x2 = ± 9 y = -12 x = 3 or x = -3 (3, 12) or (-3, -12)
  57. 57. Example 4 Solve. y = 4 − 3x  3x + y = 7 
  58. 58. Example 4 Solve. y = 4 − 3x  3x + y = 7  3x + (4 - 3x) = 7
  59. 59. Example 4 Solve. y = 4 − 3x  3x + y = 7  3x + (4 - 3x) = 7 4=7
  60. 60. Example 4 Solve. y = 4 − 3x  3x + y = 7  3x + (4 - 3x) = 7 4≠7
  61. 61. Example 4 Solve. y = 4 − 3x  3x + y = 7  3x + (4 - 3x) = 7 4≠7 Wait, what?
  62. 62. Example 4 Solve. y = 4 − 3x  3x + y = 7  3x + (4 - 3x) = 7 4≠7 Wait, what? 3x + y = 7
  63. 63. Example 4 Solve. y = 4 − 3x  3x + y = 7  3x + (4 - 3x) = 7 4≠7 Wait, what? 3x + y = 7 y = -3x + 7
  64. 64. Example 4 Solve. y = 4 − 3x  3x + y = 7  3x + (4 - 3x) = 7 4≠7 Wait, what? 3x + y = 7 y = -3x + 7 Oh, parallel lines!
  65. 65. Example 4 Solve. y = 4 − 3x  3x + y = 7  3x + (4 - 3x) = 7 4≠7 Wait, what? 3x + y = 7 y = -3x + 7 Oh, parallel lines! (No solutions)
  66. 66. Example 5 Solve. y = 2x 2   2 3y = 6x 
  67. 67. Example 5 Solve. y = 2x 2   2 3y = 6x  2 2 3(2x ) = 6x
  68. 68. Example 5 Solve. y = 2x 2   2 3y = 6x  2 2 3(2x ) = 6x 2 2 6x = 6x
  69. 69. Example 5 Solve. y = 2x 2   2 3y = 6x  2 2 3(2x ) = 6x 2 2 6x = 6x This is always true!
  70. 70. Example 5 Solve. y = 2x 2   2 3y = 6x  2 2 3(2x ) = 6x 2 2 6x = 6x This is always true! These are the same graphs.
  71. 71. Example 5 Solve. y = 2x 2   2 3y = 6x  2 2 3(2x ) = 6x 2 2 6x = 6x This is always true! These are the same graphs. Infinitely many solutions on the parabola
  72. 72. Consistent:
  73. 73. Consistent: A system with one or more solutions
  74. 74. Consistent: A system with one or more solutions Inconsistent:
  75. 75. Consistent: A system with one or more solutions Inconsistent: A systems with no solutions
  76. 76. Homework
  77. 77. Homework p. 289 #1-20, skip 17, 18 “Too many people are thinking of security instead of opportunity. They seem more afraid of life than death.” - James F. Byrnes

×