Integrated Math 2 Section 8-2

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Solve Systems of Equations Graphically

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  • Integrated Math 2 Section 8-2

    1. 1. Section 8-2 Solve Systems of Equations Graphically
    2. 2. Essential Questions How do you determine if an ordered pair is a solution of a system? How do you solve systems of linear equations graphically? Where you’ll see this: Sports, safety, economics
    3. 3. Vocabulary 1. System of Equations: 2. Solution of a System:
    4. 4. Vocabulary 1. System of Equations: Two or more equations with the same t wo variable that you solve at the same time 2. Solution of a System:
    5. 5. Vocabulary 1. System of Equations: Two or more equations with the same t wo variable that you solve at the same time 2. Solution of a System: The intersection of the t wo lines
    6. 6. Vocabulary 1. System of Equations: Two or more equations with the same t wo variable that you solve at the same time 2. Solution of a System: The intersection of the t wo lines The ordered pair that makes both equations true
    7. 7. Example 1 Tell whether the ordered pair (3, 4) is a solution to the given system. x + y = 7 a. Check by graphing  y 2 x − y = 10 x
    8. 8. Example 1 Tell whether the ordered pair (3, 4) is a solution to the given system. x + y = 7 a. Check by graphing  y 2 x − y = 10 x
    9. 9. Example 1 Tell whether the ordered pair (3, 4) is a solution to the given system. x + y = 7 a. Check by graphing  y 2 x − y = 10 x y = − x + 7  y = 2 x − 10
    10. 10. Example 1 Tell whether the ordered pair (3, 4) is a solution to the given system. x + y = 7 a. Check by graphing  y 2 x − y = 10 x y = − x + 7  y = 2 x − 10
    11. 11. Example 1 Tell whether the ordered pair (3, 4) is a solution to the given system. x + y = 7 a. Check by graphing  y 2 x − y = 10 x y = − x + 7  y = 2 x − 10
    12. 12. Example 1 Tell whether the ordered pair (3, 4) is a solution to the given system. x + y = 7 a. Check by graphing  y 2 x − y = 10 x y = − x + 7  y = 2 x − 10
    13. 13. Example 1 Tell whether the ordered pair (3, 4) is a solution to the given system. x + y = 7 a. Check by graphing  y 2 x − y = 10 x y = − x + 7  y = 2 x − 10
    14. 14. Example 1 Tell whether the ordered pair (3, 4) is a solution to the given system. x + y = 7 a. Check by graphing  y 2 x − y = 10 x y = − x + 7  y = 2 x − 10
    15. 15. Example 1 Tell whether the ordered pair (3, 4) is a solution to the given system. x + y = 7 a. Check by graphing  y 2 x − y = 10 x y = − x + 7  y = 2 x − 10
    16. 16. Example 1 Tell whether the ordered pair (3, 4) is a solution to the given system. x + y = 7 a. Check by graphing  y 2 x − y = 10 x y = − x + 7  y = 2 x − 10
    17. 17. Example 1 Tell whether the ordered pair (3, 4) is a solution to the given system. x + y = 7 a. Check by graphing  y 2 x − y = 10 x y = − x + 7  y = 2 x − 10
    18. 18. Example 1 Tell whether the ordered pair (3, 4) is a solution to the given system. x + y = 7 a. Check by graphing  y 2 x − y = 10 x y = − x + 7  y = 2 x − 10
    19. 19. Example 1 Tell whether the ordered pair (3, 4) is a solution to the given system. x + y = 7 a. Check by graphing  y 2 x − y = 10 x y = − x + 7  y = 2 x − 10
    20. 20. Example 1 Tell whether the ordered pair (3, 4) is a solution to the given system. x + y = 7 a. Check by graphing  y 2 x − y = 10 x y = − x + 7  y = 2 x − 10
    21. 21. Example 1 Tell whether the ordered pair (3, 4) is a solution to the given system. x + y = 7 a. Check by graphing  y 2 x − y = 10 x y = − x + 7  y = 2 x − 10
    22. 22. Example 1 Tell whether the ordered pair (3, 4) is a solution to the given system. x + y = 7 a. Check by graphing  y 2 x − y = 10 x y = − x + 7  y = 2 x − 10
    23. 23. Example 1 Tell whether the ordered pair (3, 4) is a solution to the given system. x + y = 7 a. Check by graphing  y 2 x − y = 10 x y = − x + 7  y = 2 x − 10
    24. 24. Example 1 Tell whether the ordered pair (3, 4) is a solution to the given system. x + y = 7 a. Check by graphing  y 2 x − y = 10 x y = − x + 7  y = 2 x − 10
    25. 25. Example 1 Tell whether the ordered pair (3, 4) is a solution to the given system. x + y = 7 a. Check by graphing  y 2 x − y = 10 x y = − x + 7  y = 2 x − 10
    26. 26. Example 1 Tell whether the ordered pair (3, 4) is a solution to the given system. x + y = 7 a. Check by graphing  y 2 x − y = 10 x y = − x + 7  y = 2 x − 10
    27. 27. Example 1 Tell whether the ordered pair (3, 4) is a solution to the given system. x + y = 7 a. Check by graphing  y 2 x − y = 10 x y = − x + 7  y = 2 x − 10
    28. 28. Example 1 Tell whether the ordered pair (3, 4) is a solution to the given system. x + y = 7 a. Check by graphing  y 2 x − y = 10 x y = − x + 7  y = 2 x − 10
    29. 29. Example 1 Tell whether the ordered pair (3, 4) is a solution to the given system. x + y = 7 a. Check by graphing  y 2 x − y = 10 x y = − x + 7  y = 2 x − 10
    30. 30. Example 1 Tell whether the ordered pair (3, 4) is a solution to the given system. x + y = 7 a. Check by graphing  y 2 x − y = 10 x y = − x + 7  y = 2 x − 10
    31. 31. Example 1 Tell whether the ordered pair (3, 4) is a solution to the given system. x + y = 7 a. Check by graphing  y 2 x − y = 10 x y = − x + 7  y = 2 x − 10
    32. 32. Example 1 Tell whether the ordered pair (3, 4) is a solution to the given system. x + y = 7 a. Check by graphing  y 2 x − y = 10 x y = − x + 7  y = 2 x − 10
    33. 33. Example 1 Tell whether the ordered pair (3, 4) is a solution to the given system. x + y = 7 a. Check by graphing  y 2 x − y = 10 Not a solution x y = − x + 7  y = 2 x − 10
    34. 34. Example 1 Tell whether the ordered pair (3, 4) is a solution to the given system. a. Check by substituting the ordered pair into the equations x + y = 7  2 x − y = 10
    35. 35. Example 1 Tell whether the ordered pair (3, 4) is a solution to the given system. a. Check by substituting the ordered pair into the equations x + y = 7  2 x − y = 10 3+4=7
    36. 36. Example 1 Tell whether the ordered pair (3, 4) is a solution to the given system. a. Check by substituting the ordered pair into the equations x + y = 7  2 x − y = 10 3+4=7 7=7
    37. 37. Example 1 Tell whether the ordered pair (3, 4) is a solution to the given system. a. Check by substituting the ordered pair into the equations x + y = 7  2 x − y = 10 3+4=7 2(3) - 4 = 10 7=7
    38. 38. Example 1 Tell whether the ordered pair (3, 4) is a solution to the given system. a. Check by substituting the ordered pair into the equations x + y = 7  2 x − y = 10 3+4=7 2(3) - 4 = 10 7=7 6 - 4 = 10
    39. 39. Example 1 Tell whether the ordered pair (3, 4) is a solution to the given system. a. Check by substituting the ordered pair into the equations x + y = 7  2 x − y = 10 3+4=7 2(3) - 4 = 10 7=7 6 - 4 = 10 2 = 10
    40. 40. Example 1 Tell whether the ordered pair (3, 4) is a solution to the given system. a. Check by substituting the ordered pair into the equations x + y = 7  2 x − y = 10 3+4=7 2(3) - 4 = 10 7=7 6 - 4 = 10 2 = 10 Not a solution
    41. 41. Example 2 Solve the system by graphing. y 2 x − y = 4  x + y = 5 x
    42. 42. Example 2 Solve the system by graphing. y 2 x − y = 4  x + y = 5 x
    43. 43. Example 2 Solve the system by graphing. y 2 x − y = 4  x + y = 5 x y = 2 x − 4  y = − x + 5
    44. 44. Example 2 Solve the system by graphing. y 2 x − y = 4  x + y = 5 x y = 2 x − 4  y = − x + 5
    45. 45. Example 2 Solve the system by graphing. y 2 x − y = 4  x + y = 5 x y = 2 x − 4  y = − x + 5
    46. 46. Example 2 Solve the system by graphing. y 2 x − y = 4  x + y = 5 x y = 2 x − 4  y = − x + 5
    47. 47. Example 2 Solve the system by graphing. y 2 x − y = 4  x + y = 5 x y = 2 x − 4  y = − x + 5
    48. 48. Example 2 Solve the system by graphing. y 2 x − y = 4  x + y = 5 x y = 2 x − 4  y = − x + 5
    49. 49. Example 2 Solve the system by graphing. y 2 x − y = 4  x + y = 5 x y = 2 x − 4  y = − x + 5
    50. 50. Example 2 Solve the system by graphing. y 2 x − y = 4  x + y = 5 x y = 2 x − 4  y = − x + 5
    51. 51. Example 2 Solve the system by graphing. y 2 x − y = 4  x + y = 5 x y = 2 x − 4  y = − x + 5
    52. 52. Example 2 Solve the system by graphing. y 2 x − y = 4  x + y = 5 x y = 2 x − 4  y = − x + 5
    53. 53. Example 2 Solve the system by graphing. y 2 x − y = 4  x + y = 5 x y = 2 x − 4  y = − x + 5
    54. 54. Example 2 Solve the system by graphing. y 2 x − y = 4  x + y = 5 x y = 2 x − 4  y = − x + 5
    55. 55. Example 2 Solve the system by graphing. y 2 x − y = 4  x + y = 5 x y = 2 x − 4  y = − x + 5
    56. 56. Example 2 Solve the system by graphing. y 2 x − y = 4  x + y = 5 x y = 2 x − 4  y = − x + 5
    57. 57. Example 2 Solve the system by graphing. y 2 x − y = 4  x + y = 5 x y = 2 x − 4  y = − x + 5
    58. 58. Example 2 Solve the system by graphing. y 2 x − y = 4  x + y = 5 x y = 2 x − 4  y = − x + 5
    59. 59. Example 2 Solve the system by graphing. y 2 x − y = 4  x + y = 5 x y = 2 x − 4  y = − x + 5
    60. 60. Example 2 Solve the system by graphing. y 2 x − y = 4  x + y = 5 x y = 2 x − 4  y = − x + 5
    61. 61. Example 2 Solve the system by graphing. y 2 x − y = 4  x + y = 5 x y = 2 x − 4  y = − x + 5
    62. 62. Example 2 Solve the system by graphing. y 2 x − y = 4  x + y = 5 x y = 2 x − 4  y = − x + 5
    63. 63. Example 2 Solve the system by graphing. y 2 x − y = 4  x + y = 5 x y = 2 x − 4  y = − x + 5
    64. 64. Example 2 Solve the system by graphing. y 2 x − y = 4  x + y = 5 x y = 2 x − 4  y = − x + 5
    65. 65. Example 2 Solve the system by graphing. y 2 x − y = 4  x + y = 5 x y = 2 x − 4  y = − x + 5
    66. 66. Example 2 Solve the system by graphing. y 2 x − y = 4  x + y = 5 x y = 2 x − 4  y = − x + 5
    67. 67. Example 2 Solve the system by graphing. y 2 x − y = 4  x + y = 5 x y = 2 x − 4  y = − x + 5
    68. 68. Example 2 Solve the system by graphing. y 2 x − y = 4  x + y = 5 x y = 2 x − 4  y = − x + 5
    69. 69. Example 2 Solve the system by graphing. y 2 x − y = 4  x + y = 5 x y = 2 x − 4  y = − x + 5
    70. 70. Example 2 Solve the system by graphing. y 2 x − y = 4  (3, 2) x + y = 5 x y = 2 x − 4  y = − x + 5
    71. 71. Example 2 Solve the system by graphing. y 2 x − y = 4  (3, 2) x + y = 5 Check: x y = 2 x − 4  y = − x + 5
    72. 72. Example 2 Solve the system by graphing. y 2 x − y = 4  (3, 2) x + y = 5 Check: x 2(3) − 2 = 4 y = 2 x − 4  y = − x + 5
    73. 73. Example 2 Solve the system by graphing. y 2 x − y = 4  (3, 2) x + y = 5 Check: x 2(3) − 2 = 4 y = 2 x − 4 6− 2 = 4  y = − x + 5
    74. 74. Example 2 Solve the system by graphing. y 2 x − y = 4  (3, 2) x + y = 5 Check: x 2(3) − 2 = 4 y = 2 x − 4 6− 2 = 4  y = − x + 5 3+2 = 5
    75. 75. Example 2 Solve the system by graphing. y 2 x − y = 4  (3, 2) x + y = 5 Check: x 2(3) − 2 = 4 y = 2 x − 4 6− 2 = 4  y = − x + 5 3+2 = 5
    76. 76. Example 3 Solve the system by graphing. y = x y  y = −3 y + x = 2  x
    77. 77. Example 3 Solve the system by graphing. y = x y  y = −3 y + x = 2  x
    78. 78. Example 3 Solve the system by graphing. y = x y  y = −3 y + x = 2  x y = x  y = −3 y = − x + 2 
    79. 79. Example 3 Solve the system by graphing. y = x y  y = −3 y + x = 2  x y = x  y = −3 y = − x + 2 
    80. 80. Example 3 Solve the system by graphing. y = x y  y = −3 y + x = 2  x y = x  y = −3 y = − x + 2 
    81. 81. Example 3 Solve the system by graphing. y = x y  y = −3 y + x = 2  x y = x  y = −3 y = − x + 2 
    82. 82. Example 3 Solve the system by graphing. y = x y  y = −3 y + x = 2  x y = x  y = −3 y = − x + 2 
    83. 83. Example 3 Solve the system by graphing. y = x y  y = −3 1 y + x = 2 A = bh  2 x y = x  y = −3 y = − x + 2 
    84. 84. Example 3 Solve the system by graphing. y = x y  y = −3 1 y + x = 2 A = bh  2 1 x A = (8)(4) 2 y = x  y = −3 y = − x + 2 
    85. 85. Example 3 Solve the system by graphing. y = x y  y = −3 1 y + x = 2 A = bh  2 1 x A = (8)(4) 2 y = x A = 16  y = −3 y = − x + 2 
    86. 86. Example 3 Solve the system by graphing. y = x y  y = −3 1 y + x = 2 A = bh  2 1 x A = (8)(4) 2 y = x A = 16 units2  y = −3 y = − x + 2 
    87. 87. Quick Question If the equations of a system are in slope-intercept form, how can you tell without graphing if the system has a solution?
    88. 88. Homework
    89. 89. Homework p. 340 #1-27 odd “If the only tool you have is a hammer, you tend to see every problem as a nail.” - Abraham Maslow

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