Int Math 2 Section 8-4 1011

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Solve Systems by Adding, Subtracting, and Multiplying (Linear Combinations)

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Int Math 2 Section 8-4 1011

  1. 1. Section 8-4 Solve Systems by Adding, Subtracting, and Multiplying (Linear Combinations)Sun, Apr 10
  2. 2. Essential Questions How do you solve systems of equations by adding and subtracting? How do you solve systems of equations by adding and multiplying? Where you’ll see this: Landscaping, construction, sportsSun, Apr 10
  3. 3. Why another method?Sun, Apr 10
  4. 4. Why another method? Graphing: Problems with accuracySun, Apr 10
  5. 5. Why another method? Graphing: Problems with accuracy Substitution: Need an isolated variableSun, Apr 10
  6. 6. Why another method? Graphing: Problems with accuracy Substitution: Need an isolated variable Combinations: Could speed up processSun, Apr 10
  7. 7. Why another method? Graphing: Problems with accuracy Substitution: Need an isolated variable Combinations: Could speed up process Look at the system to determine best methodSun, Apr 10
  8. 8. Solve by CombinationsSun, Apr 10
  9. 9. Solve by Combinations 1. Choose a variable to eliminate (your choice).Sun, Apr 10
  10. 10. Solve by Combinations 1. Choose a variable to eliminate (your choice). 2. Make the coefficients of that variable opposite. You might need to multiply to do this. Then combine equations.Sun, Apr 10
  11. 11. Solve by Combinations 1. Choose a variable to eliminate (your choice). 2. Make the coefficients of that variable opposite. You might need to multiply to do this. Then combine equations. 3. Solve for the remaining variable.Sun, Apr 10
  12. 12. Solve by Combinations 1. Choose a variable to eliminate (your choice). 2. Make the coefficients of that variable opposite. You might need to multiply to do this. Then combine equations. 3. Solve for the remaining variable. 4. Plug back into an original equation to find the other variable.Sun, Apr 10
  13. 13. Solve by Combinations 1. Choose a variable to eliminate (your choice). 2. Make the coefficients of that variable opposite. You might need to multiply to do this. Then combine equations. 3. Solve for the remaining variable. 4. Plug back into an original equation to find the other variable. 5. Check and rewrite the answer.Sun, Apr 10
  14. 14. Example 1 Solve by combining the equations ⎧−2x + 3 y = 2 ⎪ a. ⎨ ⎪ 2x + 7 y = 18 ⎩Sun, Apr 10
  15. 15. Example 1 Solve by combining the equations ⎧−2x + 3 y = 2 ⎪ a. ⎨ ⎪ 2x + 7 y = 18 ⎩ −2x + 3 y = 2Sun, Apr 10
  16. 16. Example 1 Solve by combining the equations ⎧−2x + 3 y = 2 ⎪ a. ⎨ ⎪ 2x + 7 y = 18 ⎩ −2x + 3 y = 2 2x + 7 y = 18Sun, Apr 10
  17. 17. Example 1 Solve by combining the equations ⎧−2x + 3 y = 2 ⎪ a. ⎨ ⎪ 2x + 7 y = 18 ⎩ −2x + 3 y = 2 2x + 7 y = 18Sun, Apr 10
  18. 18. Example 1 Solve by combining the equations ⎧−2x + 3 y = 2 ⎪ a. ⎨ ⎪ 2x + 7 y = 18 ⎩ −2x + 3 y = 2 2x + 7 y = 18 10 y = 20Sun, Apr 10
  19. 19. Example 1 Solve by combining the equations ⎧−2x + 3 y = 2 ⎪ a. ⎨ ⎪ 2x + 7 y = 18 ⎩ −2x + 3 y = 2 2x + 7 y = 18 10 y = 20 10 10Sun, Apr 10
  20. 20. Example 1 Solve by combining the equations ⎧−2x + 3 y = 2 ⎪ a. ⎨ ⎪ 2x + 7 y = 18 ⎩ −2x + 3 y = 2 2x + 7 y = 18 10 y = 20 10 10 y=2Sun, Apr 10
  21. 21. Example 1 Solve by combining the equations ⎧−2x + 3 y = 2 ⎪ a. ⎨ ⎪ 2x + 7 y = 18 ⎩ −2x + 3 y = 2 −2x + 3(2) = 2 2x + 7 y = 18 10 y = 20 10 10 y=2Sun, Apr 10
  22. 22. Example 1 Solve by combining the equations ⎧−2x + 3 y = 2 ⎪ a. ⎨ ⎪ 2x + 7 y = 18 ⎩ −2x + 3 y = 2 −2x + 3(2) = 2 2x + 7 y = 18 −2x + 6 = 2 10 y = 20 10 10 y=2Sun, Apr 10
  23. 23. Example 1 Solve by combining the equations ⎧−2x + 3 y = 2 ⎪ a. ⎨ ⎪ 2x + 7 y = 18 ⎩ −2x + 3 y = 2 −2x + 3(2) = 2 2x + 7 y = 18 −2x + 6 = 2 10 y = 20 −6 −6 10 10 y=2Sun, Apr 10
  24. 24. Example 1 Solve by combining the equations ⎧−2x + 3 y = 2 ⎪ a. ⎨ ⎪ 2x + 7 y = 18 ⎩ −2x + 3 y = 2 −2x + 3(2) = 2 2x + 7 y = 18 −2x + 6 = 2 10 y = 20 −6 −6 10 10 −2x = −4 y=2Sun, Apr 10
  25. 25. Example 1 Solve by combining the equations ⎧−2x + 3 y = 2 ⎪ a. ⎨ ⎪ 2x + 7 y = 18 ⎩ −2x + 3 y = 2 −2x + 3(2) = 2 2x + 7 y = 18 −2x + 6 = 2 10 y = 20 −6 −6 10 10 −2x = −4 y=2 −2 −2Sun, Apr 10
  26. 26. Example 1 Solve by combining the equations ⎧−2x + 3 y = 2 ⎪ a. ⎨ ⎪ 2x + 7 y = 18 ⎩ −2x + 3 y = 2 −2x + 3(2) = 2 2x + 7 y = 18 −2x + 6 = 2 10 y = 20 −6 −6 10 10 −2x = −4 y=2 −2 −2 x=2Sun, Apr 10
  27. 27. Example 1 Solve by combining the equations ⎧−2x + 3 y = 2 ⎪ a. ⎨ ⎪ 2x + 7 y = 18 ⎩ Check: −2x + 3 y = 2 −2x + 3(2) = 2 2x + 7 y = 18 −2x + 6 = 2 10 y = 20 −6 −6 10 10 −2x = −4 y=2 −2 −2 x=2Sun, Apr 10
  28. 28. Example 1 Solve by combining the equations ⎧−2x + 3 y = 2 ⎪ a. ⎨ ⎪ 2x + 7 y = 18 ⎩ Check: −2x + 3 y = 2 −2(2) + 3(2) = 2 −2x + 3(2) = 2 2x + 7 y = 18 −2x + 6 = 2 10 y = 20 −6 −6 10 10 −2x = −4 y=2 −2 −2 x=2Sun, Apr 10
  29. 29. Example 1 Solve by combining the equations ⎧−2x + 3 y = 2 ⎪ a. ⎨ ⎪ 2x + 7 y = 18 ⎩ Check: −2x + 3 y = 2 −2(2) + 3(2) = 2 −2x + 3(2) = 2 2x + 7 y = 18 −4 + 6 = 2 −2x + 6 = 2 10 y = 20 −6 −6 10 10 −2x = −4 y=2 −2 −2 x=2Sun, Apr 10
  30. 30. Example 1 Solve by combining the equations ⎧−2x + 3 y = 2 ⎪ a. ⎨ ⎪ 2x + 7 y = 18 ⎩ Check: −2x + 3 y = 2 −2(2) + 3(2) = 2 −2x + 3(2) = 2 2x + 7 y = 18 −4 + 6 = 2 −2x + 6 = 2 10 y = 20 −6 −6 2(2) + 7(2) = 18 10 10 −2x = −4 y=2 −2 −2 x=2Sun, Apr 10
  31. 31. Example 1 Solve by combining the equations ⎧−2x + 3 y = 2 ⎪ a. ⎨ ⎪ 2x + 7 y = 18 ⎩ Check: −2x + 3 y = 2 −2(2) + 3(2) = 2 −2x + 3(2) = 2 2x + 7 y = 18 −4 + 6 = 2 −2x + 6 = 2 10 y = 20 −6 −6 2(2) + 7(2) = 18 10 10 −2x = −4 4 + 14 = 18 y=2 −2 −2 x=2Sun, Apr 10
  32. 32. Example 1 Solve by combining the equations ⎧−2x + 3 y = 2 ⎪ a. ⎨ ⎪ 2x + 7 y = 18 ⎩ Check: −2x + 3 y = 2 −2(2) + 3(2) = 2 −2x + 3(2) = 2 2x + 7 y = 18 −4 + 6 = 2 −2x + 6 = 2 10 y = 20 −6 −6 2(2) + 7(2) = 18 10 10 −2x = −4 4 + 14 = 18 y=2 −2 −2 x=2 (2, 2)Sun, Apr 10
  33. 33. Example 1 Solve by combining the equations ⎧10x + 4 y = 14 ⎪ b. ⎨ ⎪x + 4 y = 5 ⎩Sun, Apr 10
  34. 34. Example 1 Solve by combining the equations ⎧10x + 4 y = 14 ⎪ b. ⎨ ⎪ x + 4 y = 5)(−1) ⎩(Sun, Apr 10
  35. 35. Example 1 Solve by combining the equations ⎧10x + 4 y = 14 ⎪ b. ⎨ ⎪ x + 4 y = 5)(−1) ⎩( 10x + 4 y = 14Sun, Apr 10
  36. 36. Example 1 Solve by combining the equations ⎧10x + 4 y = 14 ⎪ b. ⎨ ⎪ x + 4 y = 5)(−1) ⎩( 10x + 4 y = 14 − x − 4 y = −5Sun, Apr 10
  37. 37. Example 1 Solve by combining the equations ⎧10x + 4 y = 14 ⎪ b. ⎨ ⎪ x + 4 y = 5)(−1) ⎩( 10x + 4 y = 14 − x − 4 y = −5Sun, Apr 10
  38. 38. Example 1 Solve by combining the equations ⎧10x + 4 y = 14 ⎪ b. ⎨ ⎪ x + 4 y = 5)(−1) ⎩( 10x + 4 y = 14 − x − 4 y = −5 9x = 9Sun, Apr 10
  39. 39. Example 1 Solve by combining the equations ⎧10x + 4 y = 14 ⎪ b. ⎨ ⎪ x + 4 y = 5)(−1) ⎩( 10x + 4 y = 14 − x − 4 y = −5 9x = 9 9 9Sun, Apr 10
  40. 40. Example 1 Solve by combining the equations ⎧10x + 4 y = 14 ⎪ b. ⎨ ⎪ x + 4 y = 5)(−1) ⎩( 10x + 4 y = 14 − x − 4 y = −5 9x = 9 9 9 x=1Sun, Apr 10
  41. 41. Example 1 Solve by combining the equations ⎧10x + 4 y = 14 ⎪ b. ⎨ ⎪ x + 4 y = 5)(−1) ⎩( 10x + 4 y = 14 − x − 4 y = −5 1+ 4 y = 5 9x = 9 9 9 x=1Sun, Apr 10
  42. 42. Example 1 Solve by combining the equations ⎧10x + 4 y = 14 ⎪ b. ⎨ ⎪ x + 4 y = 5)(−1) ⎩( 10x + 4 y = 14 − x − 4 y = −5 1+ 4 y = 5 9x = 9 −1 −1 9 9 x=1Sun, Apr 10
  43. 43. Example 1 Solve by combining the equations ⎧10x + 4 y = 14 ⎪ b. ⎨ ⎪ x + 4 y = 5)(−1) ⎩( 10x + 4 y = 14 − x − 4 y = −5 1+ 4 y = 5 9x = 9 −1 −1 9 9 4y = 4 x=1Sun, Apr 10
  44. 44. Example 1 Solve by combining the equations ⎧10x + 4 y = 14 ⎪ b. ⎨ ⎪ x + 4 y = 5)(−1) ⎩( 10x + 4 y = 14 − x − 4 y = −5 1+ 4 y = 5 9x = 9 −1 −1 9 9 4y = 4 4 4 x=1Sun, Apr 10
  45. 45. Example 1 Solve by combining the equations ⎧10x + 4 y = 14 ⎪ b. ⎨ ⎪ x + 4 y = 5)(−1) ⎩( 10x + 4 y = 14 − x − 4 y = −5 1+ 4 y = 5 9x = 9 −1 −1 9 9 4y = 4 4 4 x=1 y =1Sun, Apr 10
  46. 46. Example 1 Solve by combining the equations ⎧10x + 4 y = 14 ⎪ b. ⎨ ⎪ x + 4 y = 5)(−1) ⎩( Check: 10x + 4 y = 14 − x − 4 y = −5 1+ 4 y = 5 9x = 9 −1 −1 9 9 4y = 4 4 4 x=1 y =1Sun, Apr 10
  47. 47. Example 1 Solve by combining the equations ⎧10x + 4 y = 14 ⎪ b. ⎨ ⎪ x + 4 y = 5)(−1) ⎩( Check: 10x + 4 y = 14 − x − 4 y = −5 1+ 4 y = 5 10(1) + 4(1) = 14 9x = 9 −1 −1 9 9 4y = 4 4 4 x=1 y =1Sun, Apr 10
  48. 48. Example 1 Solve by combining the equations ⎧10x + 4 y = 14 ⎪ b. ⎨ ⎪ x + 4 y = 5)(−1) ⎩( Check: 10x + 4 y = 14 − x − 4 y = −5 1+ 4 y = 5 10(1) + 4(1) = 14 9x = 9 −1 −1 10 + 4 = 14 9 9 4y = 4 4 4 x=1 y =1Sun, Apr 10
  49. 49. Example 1 Solve by combining the equations ⎧10x + 4 y = 14 ⎪ b. ⎨ ⎪ x + 4 y = 5)(−1) ⎩( Check: 10x + 4 y = 14 − x − 4 y = −5 1+ 4 y = 5 10(1) + 4(1) = 14 9x = 9 −1 −1 10 + 4 = 14 9 9 4y = 4 4 4 1 + 4(1) = 5 x=1 y =1Sun, Apr 10
  50. 50. Example 1 Solve by combining the equations ⎧10x + 4 y = 14 ⎪ b. ⎨ ⎪ x + 4 y = 5)(−1) ⎩( Check: 10x + 4 y = 14 − x − 4 y = −5 1+ 4 y = 5 10(1) + 4(1) = 14 9x = 9 −1 −1 10 + 4 = 14 9 9 4y = 4 4 4 1 + 4(1) = 5 x=1 1+ 4 = 5 y =1Sun, Apr 10
  51. 51. Example 1 Solve by combining the equations ⎧10x + 4 y = 14 ⎪ b. ⎨ ⎪ x + 4 y = 5)(−1) ⎩( Check: 10x + 4 y = 14 − x − 4 y = −5 1+ 4 y = 5 10(1) + 4(1) = 14 9x = 9 −1 −1 10 + 4 = 14 9 9 4y = 4 4 4 1 + 4(1) = 5 x=1 1+ 4 = 5 y =1 (1,1)Sun, Apr 10
  52. 52. Example 2 Solve by combining the equations ⎧7x + 2 y = 5 ⎪ ⎨ ⎪ 2x + 3 y = 16 ⎩Sun, Apr 10
  53. 53. Example 2 Solve by combining the equations ⎧7x + 2 y = 5)(3) ⎪( ⎨ ⎪ 2x + 3 y = 16 ⎩Sun, Apr 10
  54. 54. Example 2 Solve by combining the equations ⎧7x + 2 y = 5)(3) ⎪( ⎨ ⎪ 2x + 3 y = 16)(−2) ⎩(Sun, Apr 10
  55. 55. Example 2 Solve by combining the equations ⎧7x + 2 y = 5)(3) ⎪( ⎨ ⎪ 2x + 3 y = 16)(−2) ⎩( 21x + 6 y = 15Sun, Apr 10
  56. 56. Example 2 Solve by combining the equations ⎧7x + 2 y = 5)(3) ⎪( ⎨ ⎪ 2x + 3 y = 16)(−2) ⎩( 21x + 6 y = 15 −4x − 6 y = −32Sun, Apr 10
  57. 57. Example 2 Solve by combining the equations ⎧7x + 2 y = 5)(3) ⎪( ⎨ ⎪ 2x + 3 y = 16)(−2) ⎩( 21x + 6 y = 15 −4x − 6 y = −32Sun, Apr 10
  58. 58. Example 2 Solve by combining the equations ⎧7x + 2 y = 5)(3) ⎪( ⎨ ⎪ 2x + 3 y = 16)(−2) ⎩( 21x + 6 y = 15 −4x − 6 y = −32 17x = −17Sun, Apr 10
  59. 59. Example 2 Solve by combining the equations ⎧7x + 2 y = 5)(3) ⎪( ⎨ ⎪ 2x + 3 y = 16)(−2) ⎩( 21x + 6 y = 15 −4x − 6 y = −32 17x = −17 17 17Sun, Apr 10
  60. 60. Example 2 Solve by combining the equations ⎧7x + 2 y = 5)(3) ⎪( ⎨ ⎪ 2x + 3 y = 16)(−2) ⎩( 21x + 6 y = 15 −4x − 6 y = −32 17x = −17 17 17 x = −1Sun, Apr 10
  61. 61. Example 2 Solve by combining the equations ⎧7x + 2 y = 5)(3) ⎪( ⎨ ⎪ 2x + 3 y = 16)(−2) ⎩( 21x + 6 y = 15 2(−1) + 3 y = 16 −4x − 6 y = −32 17x = −17 17 17 x = −1Sun, Apr 10
  62. 62. Example 2 Solve by combining the equations ⎧7x + 2 y = 5)(3) ⎪( ⎨ ⎪ 2x + 3 y = 16)(−2) ⎩( 21x + 6 y = 15 2(−1) + 3 y = 16 −4x − 6 y = −32 −2 + 3 y = 16 17x = −17 17 17 x = −1Sun, Apr 10
  63. 63. Example 2 Solve by combining the equations ⎧7x + 2 y = 5)(3) ⎪( ⎨ ⎪ 2x + 3 y = 16)(−2) ⎩( 21x + 6 y = 15 2(−1) + 3 y = 16 −4x − 6 y = −32 −2 + 3 y = 16 17x = −17 +2 +2 17 17 x = −1Sun, Apr 10
  64. 64. Example 2 Solve by combining the equations ⎧7x + 2 y = 5)(3) ⎪( ⎨ ⎪ 2x + 3 y = 16)(−2) ⎩( 21x + 6 y = 15 2(−1) + 3 y = 16 −4x − 6 y = −32 −2 + 3 y = 16 17x = −17 +2 +2 17 17 3 y = 18 x = −1Sun, Apr 10
  65. 65. Example 2 Solve by combining the equations ⎧7x + 2 y = 5)(3) ⎪( ⎨ ⎪ 2x + 3 y = 16)(−2) ⎩( 21x + 6 y = 15 2(−1) + 3 y = 16 −4x − 6 y = −32 −2 + 3 y = 16 17x = −17 +2 +2 17 17 3 y = 18 x = −1 3 3Sun, Apr 10
  66. 66. Example 2 Solve by combining the equations ⎧7x + 2 y = 5)(3) ⎪( ⎨ ⎪ 2x + 3 y = 16)(−2) ⎩( 21x + 6 y = 15 2(−1) + 3 y = 16 −4x − 6 y = −32 −2 + 3 y = 16 17x = −17 +2 +2 17 17 3 y = 18 x = −1 3 3 y=6Sun, Apr 10
  67. 67. Example 2 Solve by combining the equations ⎧7x + 2 y = 5)(3) ⎪( ⎨ ⎪ 2x + 3 y = 16)(−2) ⎩( Check: 21x + 6 y = 15 2(−1) + 3 y = 16 −4x − 6 y = −32 −2 + 3 y = 16 17x = −17 +2 +2 17 17 3 y = 18 x = −1 3 3 y=6Sun, Apr 10
  68. 68. Example 2 Solve by combining the equations ⎧7x + 2 y = 5)(3) ⎪( ⎨ ⎪ 2x + 3 y = 16)(−2) ⎩( Check: 21x + 6 y = 15 2(−1) + 3 y = 16 −4x − 6 y = −32 7(−1) + 2(6) = 5 −2 + 3 y = 16 17x = −17 +2 +2 17 17 3 y = 18 x = −1 3 3 y=6Sun, Apr 10
  69. 69. Example 2 Solve by combining the equations ⎧7x + 2 y = 5)(3) ⎪( ⎨ ⎪ 2x + 3 y = 16)(−2) ⎩( Check: 21x + 6 y = 15 2(−1) + 3 y = 16 −4x − 6 y = −32 7(−1) + 2(6) = 5 −2 + 3 y = 16 +2 −7 + 12 = 5 17x = −17 +2 17 17 3 y = 18 x = −1 3 3 y=6Sun, Apr 10
  70. 70. Example 2 Solve by combining the equations ⎧7x + 2 y = 5)(3) ⎪( ⎨ ⎪ 2x + 3 y = 16)(−2) ⎩( Check: 21x + 6 y = 15 2(−1) + 3 y = 16 −4x − 6 y = −32 7(−1) + 2(6) = 5 −2 + 3 y = 16 +2 −7 + 12 = 5 17x = −17 +2 17 17 3 y = 18 2(−1) + 3(6) = 16 x = −1 3 3 y=6Sun, Apr 10
  71. 71. Example 2 Solve by combining the equations ⎧7x + 2 y = 5)(3) ⎪( ⎨ ⎪ 2x + 3 y = 16)(−2) ⎩( Check: 21x + 6 y = 15 2(−1) + 3 y = 16 −4x − 6 y = −32 7(−1) + 2(6) = 5 −2 + 3 y = 16 +2 −7 + 12 = 5 17x = −17 +2 17 17 3 y = 18 2(−1) + 3(6) = 16 x = −1 3 3 −2 + 18 = 16 y=6Sun, Apr 10
  72. 72. Example 2 Solve by combining the equations ⎧7x + 2 y = 5)(3) ⎪( ⎨ ⎪ 2x + 3 y = 16)(−2) ⎩( Check: 21x + 6 y = 15 2(−1) + 3 y = 16 −4x − 6 y = −32 7(−1) + 2(6) = 5 −2 + 3 y = 16 +2 −7 + 12 = 5 17x = −17 +2 17 17 3 y = 18 2(−1) + 3(6) = 16 x = −1 3 3 −2 + 18 = 16 y=6 (−1, 6)Sun, Apr 10
  73. 73. Example 3 Solve by combining the equations ⎧5x + 2 y = 7 ⎪ ⎨ ⎪4x + 2 y = −3 ⎩Sun, Apr 10
  74. 74. Example 3 Solve by combining the equations ⎧5x + 2 y = 7 ⎪ ⎨ ⎪4x + 2 y = −3)(−1) ⎩(Sun, Apr 10
  75. 75. Example 3 Solve by combining the equations ⎧5x + 2 y = 7 ⎪ ⎨ ⎪4x + 2 y = −3)(−1) ⎩( 5x + 2 y = 7Sun, Apr 10
  76. 76. Example 3 Solve by combining the equations ⎧5x + 2 y = 7 ⎪ ⎨ ⎪4x + 2 y = −3)(−1) ⎩( 5x + 2 y = 7 −4x − 2 y = 3Sun, Apr 10
  77. 77. Example 3 Solve by combining the equations ⎧5x + 2 y = 7 ⎪ ⎨ ⎪4x + 2 y = −3)(−1) ⎩( 5x + 2 y = 7 −4x − 2 y = 3Sun, Apr 10
  78. 78. Example 3 Solve by combining the equations ⎧5x + 2 y = 7 ⎪ ⎨ ⎪4x + 2 y = −3)(−1) ⎩( 5x + 2 y = 7 −4x − 2 y = 3 x = 10Sun, Apr 10
  79. 79. Example 3 Solve by combining the equations ⎧5x + 2 y = 7 ⎪ ⎨ ⎪4x + 2 y = −3)(−1) ⎩( 5x + 2 y = 7 5(10) + 2 y = 7 −4x − 2 y = 3 x = 10Sun, Apr 10
  80. 80. Example 3 Solve by combining the equations ⎧5x + 2 y = 7 ⎪ ⎨ ⎪4x + 2 y = −3)(−1) ⎩( 5x + 2 y = 7 5(10) + 2 y = 7 −4x − 2 y = 3 50 + 2 y = 7 x = 10Sun, Apr 10
  81. 81. Example 3 Solve by combining the equations ⎧5x + 2 y = 7 ⎪ ⎨ ⎪4x + 2 y = −3)(−1) ⎩( 5x + 2 y = 7 5(10) + 2 y = 7 −4x − 2 y = 3 50 + 2 y = 7 −50 −50 x = 10Sun, Apr 10
  82. 82. Example 3 Solve by combining the equations ⎧5x + 2 y = 7 ⎪ ⎨ ⎪4x + 2 y = −3)(−1) ⎩( 5x + 2 y = 7 5(10) + 2 y = 7 −4x − 2 y = 3 50 + 2 y = 7 −50 −50 x = 10 2 y = −43Sun, Apr 10
  83. 83. Example 3 Solve by combining the equations ⎧5x + 2 y = 7 ⎪ ⎨ ⎪4x + 2 y = −3)(−1) ⎩( 5x + 2 y = 7 5(10) + 2 y = 7 −4x − 2 y = 3 50 + 2 y = 7 −50 −50 x = 10 2 y = −43 2 2Sun, Apr 10
  84. 84. Example 3 Solve by combining the equations ⎧5x + 2 y = 7 ⎪ ⎨ ⎪4x + 2 y = −3)(−1) ⎩( 5x + 2 y = 7 5(10) + 2 y = 7 −4x − 2 y = 3 50 + 2 y = 7 −50 −50 x = 10 2 y = −43 2 2 −43 y= 2Sun, Apr 10
  85. 85. Example 3 Solve by combining the equations ⎧5x + 2 y = 7 ⎪ ⎨ ⎪4x + 2 y = −3)(−1) ⎩( Check: 5x + 2 y = 7 5(10) + 2 y = 7 −4x − 2 y = 3 50 + 2 y = 7 −50 −50 x = 10 2 y = −43 2 2 −43 y= 2Sun, Apr 10
  86. 86. Example 3 Solve by combining the equations ⎧5x + 2 y = 7 ⎪ ⎨ ⎪4x + 2 y = −3)(−1) ⎩( Check: 5x + 2 y = 7 5(10) + 2 y = 7 5(10) + 2(− ) = 7 43 −4x − 2 y = 3 50 + 2 y = 7 2 −50 −50 x = 10 2 y = −43 2 2 −43 y= 2Sun, Apr 10
  87. 87. Example 3 Solve by combining the equations ⎧5x + 2 y = 7 ⎪ ⎨ ⎪4x + 2 y = −3)(−1) ⎩( Check: 5x + 2 y = 7 5(10) + 2 y = 7 5(10) + 2(− ) = 7 43 −4x − 2 y = 3 50 + 2 y = 7 2 −50 50 − 43 = 7 −50 x = 10 2 y = −43 2 2 −43 y= 2Sun, Apr 10
  88. 88. Example 3 Solve by combining the equations ⎧5x + 2 y = 7 ⎪ ⎨ ⎪4x + 2 y = −3)(−1) ⎩( Check: 5x + 2 y = 7 5(10) + 2 y = 7 5(10) + 2(− ) = 7 43 −4x − 2 y = 3 50 + 2 y = 7 2 −50 50 − 43 = 7 −50 x = 10 2 y = −43 4(10) + 2(− ) = −3 43 2 2 2 −43 y= 2Sun, Apr 10
  89. 89. Example 3 Solve by combining the equations ⎧5x + 2 y = 7 ⎪ ⎨ ⎪4x + 2 y = −3)(−1) ⎩( Check: 5x + 2 y = 7 5(10) + 2 y = 7 5(10) + 2(− ) = 7 43 −4x − 2 y = 3 50 + 2 y = 7 2 −50 50 − 43 = 7 −50 x = 10 2 y = −43 4(10) + 2(− ) = −3 43 2 2 2 40 − 43 = −3 −43 y= 2Sun, Apr 10
  90. 90. Example 3 Solve by combining the equations ⎧5x + 2 y = 7 ⎪ ⎨ ⎪4x + 2 y = −3)(−1) ⎩( Check: 5x + 2 y = 7 5(10) + 2 y = 7 5(10) + 2(− ) = 7 43 −4x − 2 y = 3 50 + 2 y = 7 2 −50 50 − 43 = 7 −50 x = 10 2 y = −43 4(10) + 2(− ) = −3 43 2 2 2 40 − 43 = −3 −43 y= 2 (10, − ) 43 2Sun, Apr 10
  91. 91. Problem SetSun, Apr 10
  92. 92. Problem Set p. 350 #1-27 odd “A verbal contract isn’t worth the paper it’s written on.” - Samuel GoldwynSun, Apr 10

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