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Solve Linear Equations

Solve Linear Equations
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2017-03-06 12:05
FunctionCoordinate GeometryGeometric Construction
This example demonstrates the process of solving linear equations. The core mathematical concepts involved include methods for solving linear equations. Using GeoGebra commands such as Segment, If, Length, Sequence, Circle, and Sum, the geometric representation of linear equations can be constructed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Segment(C1, C2) → E2
  2. Segment(C1, C3) → E1
  3. Segment(C3, C2) → E3
  4. Segment(C4, C2) → E5
  5. Segment(C3, C4) → E4
  6. Segment(C4, C5) → E6
  7. Segment(C5, C6) → E8
  8. Segment(C5, C7) → E7
  9. Segment(C6, C7) → E9
  10. Segment(C6, C8) → E11
  11. Segment(C7, C8) → E10
  12. Segment(C8, C9) → E12
  13. Segment(C9, C10) → E15
  14. Segment(C10, C11) → E16
  15. Segment(C10, C12) → E18
  16. Segment(C11, C12) → E17
  17. Segment(C12, C13) → E19
  18. Segment(C14, C1) → E23
  19. Segment(C13, C14) → E20
  20. Segment(C13, C15) → E21
  21. Segment(C14, C15) → E22
  22. If(level ≟ true, Segment[C9, C1], Segment[C1, C15]) → E14
  23. If(level ≟ true, Segment[C9, C2], Segment[C9, C11]) → E13
  24. If(level ≟ false, {E1, E2, E3, E4, E5, E6, E7, E8, E9, E10, E11, E12, E13, E14, E15, E16, E17, E18, E19, E20, E21, E22, E23}, {E1, E2, E3, E4, E5, E6, E7, E8, E9, E10, E11, E12, E13, E14}) → list1
  25. Length(list1) → numb
  26. Sequence(Intersect[E1, Element[list1, i]], i, 1, numb) → F1
  27. Circle((0, 0), 1) → c
  28. Sequence(Intersect[E2, Element[list1, i]], i, 1, numb) → F2
  29. Sequence(Intersect[E3, Element[list1, i]], i, 1, numb) → F3
  30. Sequence(Intersect[E4, Element[list1, i]], i, 1, numb) → F4
  31. Sequence(Intersect[E5, Element[list1, i]], i, 1, numb) → F5
  32. Sequence(Intersect[E6, Element[list1, i]], i, 1, numb) → F6
  33. Sequence(Intersect[E7, Element[list1, i]], i, 1, numb) → F7
  34. Sequence(Intersect[E8, Element[list1, i]], i, 1, numb) → F8
  35. Sequence(Intersect[E9, Element[list1, i]], i, 1, numb) → F9
  36. Sequence(Intersect[E10, Element[list1, i]], i, 1, numb) → F10
  37. Sequence(Intersect[E11, Element[list1, i]], i, 1, numb) → F11
  38. Sequence(Intersect[E12, Element[list1, i]], i, 1, numb) → F12
  39. Sequence(Intersect[E13, Element[list1, i]], i, 1, numb) → F13
  40. Sequence(Intersect[E14, Element[list1, i]], i, 1, numb) → F14
  41. Sequence(Intersect[E15, Element[list1, i]], i, 1, numb) → F15
  42. Sequence(Intersect[E16, Element[list1, i]], i, 1, numb) → F16
  43. Sequence(Intersect[E17, Element[list1, i]], i, 1, numb) → F17
  44. Sequence(Intersect[E18, Element[list1, i]], i, 1, numb) → F18
  45. Sequence(Intersect[E19, Element[list1, i]], i, 1, numb) → F19
  46. Sequence(Intersect[E20, Element[list1, i]], i, 1, numb) → F20
  47. Sequence(Intersect[E21, Element[list1, i]], i, 1, numb) → F21
  48. Sequence(Intersect[E22, Element[list1, i]], i, 1, numb) → F22
  49. Sequence(Intersect[E23, Element[list1, i]], i, 1, numb) → F23
  50. Sequence(If[Element[F1, i] ≠ Element[F1, i], (0, 0), Element[F1, i]], i, 1, numb) → G1
  51. Sequence(If[Element[F2, i] ≠ Element[F2, i], (0, 0), Element[F2, i]], i, 1, numb) → G2
  52. Sequence(If[Element[F3, i] ≠ Element[F3, i], (0, 0), Element[F3, i]], i, 1, numb) → G3
  53. Sequence(If[Element[F4, i] ≠ Element[F4, i], (0, 0), Element[F4, i]], i, 1, numb) → G4
  54. Sequence(If[Element[F5, i] ≠ Element[F5, i], (0, 0), Element[F5, i]], i, 1, numb) → G5
  55. Sequence(If[Element[F6, i] ≠ Element[F6, i], (0, 0), Element[F6, i]], i, 1, numb) → G6
  56. Sequence(If[Element[F7, i] ≠ Element[F7, i], (0, 0), Element[F7, i]], i, 1, numb) → G7
  57. Sequence(If[Element[F8, i] ≠ Element[F8, i], (0, 0), Element[F8, i]], i, 1, numb) → G8
  58. Sequence(If[Element[F9, i] ≠ Element[F9, i], (0, 0), Element[F9, i]], i, 1, numb) → G9
  59. Sequence(If[Element[F10, i] ≠ Element[F10, i], (0, 0), Element[F10, i]], i, 1, numb) → G10
  60. Sequence(If[Element[F11, i] ≠ Element[F11, i], (0, 0), Element[F11, i]], i, 1, numb) → G11
  61. Sequence(If[Element[F12, i] ≠ Element[F12, i], (0, 0), Element[F12, i]], i, 1, numb) → G12
  62. Sequence(If[Element[F13, i] ≠ Element[F13, i], (0, 0), Element[F13, i]], i, 1, numb) → G13
  63. Sequence(If[Element[F14, i] ≠ Element[F14, i], (0, 0), Element[F14, i]], i, 1, numb) → G14
  64. Sequence(If[Element[F15, i] ≠ Element[F15, i], (0, 0), Element[F15, i]], i, 1, numb) → G15
  65. Sequence(If[Element[G1, i] ≟ (0, 0), 1, 0], i, 1, numb) → H1
  66. Sequence(If[Element[G2, i] ≟ (0, 0), 1, 0], i, 1, numb) → H2
  67. Sequence(If[Element[G3, i] ≟ (0, 0), 1, 0], i, 1, numb) → H3
  68. Sequence(If[Element[G4, i] ≟ (0, 0), 1, 0], i, 1, numb) → H4
  69. Sequence(If[Element[G5, i] ≟ (0, 0), 1, 0], i, 1, numb) → H5
  70. Sequence(If[Element[G6, i] ≟ (0, 0), 1, 0], i, 1, numb) → H6
  71. Sequence(If[Element[G7, i] ≟ (0, 0), 1, 0], i, 1, numb) → H7
  72. Sequence(If[Element[G8, i] ≟ (0, 0), 1, 0], i, 1, numb) → H8
  73. Sequence(If[Element[G9, i] ≟ (0, 0), 1, 0], i, 1, numb) → H9
  74. Sequence(If[Element[G10, i] ≟ (0, 0), 1, 0], i, 1, numb) → H10
  75. Sequence(If[Element[G11, i] ≟ (0, 0), 1, 0], i, 1, numb) → H11
  76. Sequence(If[Element[G12, i] ≟ (0, 0), 1, 0], i, 1, numb) → H12
  77. Sequence(If[Element[G13, i] ≟ (0, 0), 1, 0], i, 1, numb) → H13
  78. Sequence(If[Element[G14, i] ≟ (0, 0), 1, 0], i, 1, numb) → H14
  79. Sequence(If[Element[G15, i] ≟ (0, 0), 1, 0], i, 1, numb) → H15
  80. Sequence(If[Element[F16, i] ≠ Element[F16, i], (0, 0), Element[F16, i]], i, 1, numb) → G16
  81. Sequence(If[Element[F17, i] ≠ Element[F17, i], (0, 0), Element[F17, i]], i, 1, numb) → G17
  82. Sequence(If[Element[F18, i] ≠ Element[F18, i], (0, 0), Element[F18, i]], i, 1, numb) → G18
  83. Sequence(If[Element[F19, i] ≠ Element[F19, i], (0, 0), Element[F19, i]], i, 1, numb) → G19
  84. Sequence(If[Element[F20, i] ≠ Element[F20, i], (0, 0), Element[F20, i]], i, 1, numb) → G20
  85. Sequence(If[Element[F21, i] ≠ Element[F21, i], (0, 0), Element[F21, i]], i, 1, numb) → G21
  86. Sequence(If[Element[F22, i] ≠ Element[F22, i], (0, 0), Element[F22, i]], i, 1, numb) → G22
  87. Sequence(If[Element[F23, i] ≠ Element[F23, i], (0, 0), Element[F23, i]], i, 1, numb) → G23
  88. Sequence(If[Element[G16, i] ≟ (0, 0), 1, 0], i, 1, numb) → H16
  89. Sequence(If[Element[G17, i] ≟ (0, 0), 1, 0], i, 1, numb) → H17
  90. Sequence(If[Element[G18, i] ≟ (0, 0), 1, 0], i, 1, numb) → H18
  91. Sequence(If[Element[G19, i] ≟ (0, 0), 1, 0], i, 1, numb) → H19
  92. Sequence(If[Element[G20, i] ≟ (0, 0), 1, 0], i, 1, numb) → H20
  93. Sequence(If[Element[G21, i] ≟ (0, 0), 1, 0], i, 1, numb) → H21
  94. Sequence(If[Element[G22, i] ≟ (0, 0), 1, 0], i, 1, numb) → H22
  95. Sequence(If[Element[G23, i] ≟ (0, 0), 1, 0], i, 1, numb) → H23
  96. Sum(H1) → I1
  97. Sum(H2) → I2
  98. Sum(H3) → I3
  99. Sum(H4) → I4
  100. Sum(H5) → I5
  101. Sum(H6) → I6
  102. Sum(H7) → I7
  103. Sum(H8) → I8
  104. Sum(H9) → I9
  105. Sum(H10) → I10
  106. Sum(H11) → I11
  107. Sum(H12) → I12
  108. Sum(H13) → I13
  109. Sum(H14) → I14
  110. Sum(H15) → I15
  111. Sum(H16) → I16
  112. Sum(H17) → I17
  113. Sum(H18) → I18
  114. Sum(H19) → I19
  115. Sum(H20) → I20
  116. Sum(H21) → I21
  117. Sum(H22) → I22
  118. If(level ≟ true, Sum[list2], Sum[list4]) → a
  119. Sum(H23) → I23