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Systems of Equations

Systems of Equations
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2017-08-20 19:37
Coordinate GeometryGeometric Construction
This example demonstrates the geometric representation of systems of equations. It involves key mathematical concepts such as solving linear equation systems. Using GeoGebra commands like LaTeX, If, Shuffle, etc., it dynamically shows how the solutions of the system change with parameter variations. Suitable for middle school and above students to learn linear algebra and coordinate geometry.

GeoGebra Commands & Parameters

  1. LaTeX("x") → F17
  2. LaTeX("\begin{array}{} 3x+4y=-23 \\ 3x-2y=-29 \end{array} ") → D17
  3. LaTeX("\begin{array}{} 3x-5y=-62 \\ -5x+y=30 \end{array} ") → D16
  4. LaTeX("x") → F16
  5. LaTeX("\begin{array}{} 2x-2y=44 \\ 4x+2y=-14 \end{array} ") → D15
  6. LaTeX("x") → F15
  7. LaTeX("\begin{array}{} x+5y=-53 \\ 5x-3y=71 \end{array} ") → D14
  8. LaTeX("x") → F14
  9. LaTeX("\begin{array}{} 2x-3y=13 \\ -5x+2y=28 \end{array} ") → B14
  10. If(n ≟ 1, B14, If[n ≟ 2, D14, If[n ≟ 3, F14, ""]]) → A14
  11. LaTeX("\begin{array}{} x+3y=2 \\ 4x-y=21 \end{array} ") → B15
  12. If(n ≟ 1, B15, If[n ≟ 2, D15, If[n ≟ 3, F15, ""]]) → A15
  13. LaTeX("\begin{array}{} 3x+2y=-6 \\ 4x-3y=43 \end{array} ") → B16
  14. If(n ≟ 1, B16, If[n ≟ 2, D16, If[n ≟ 3, F16, ""]]) → A16
  15. LaTeX("\begin{array}{} 2x-5y=0 \\ -5x+y=92 \end{array} ") → B17
  16. If(n ≟ 1, B17, If[n ≟ 2, D17, If[n ≟ 3, F17, ""]]) → A17
  17. LaTeX("\begin{array}{} 2x-5y=80 \\ 2x+y=32 \end{array} ") → D18
  18. LaTeX("x") → F18
  19. LaTeX("\begin{array}{} 3x-2y=-10 \\ -2x+y=2 \end{array} ") → D19
  20. LaTeX("x") → F19
  21. LaTeX("\begin{array}{} 3x+3y=-33 \\ 5x-2y=36 \end{array} ") → D20
  22. LaTeX("x") → F20
  23. LaTeX("\begin{array}{} x-3y=24 \\ 3x+y=42 \end{array} ") → D21
  24. LaTeX("x") → F21
  25. LaTeX("\begin{array}{} 2x-5y=117 \\ -2x+3y=-79 \end{array} ") → D22
  26. LaTeX("x") → F22
  27. LaTeX("\begin{array}{} 2x+5y=-58 \\ 5x-y=98 \end{array} ") → D23
  28. LaTeX("x") → F23
  29. LaTeX("\begin{array}{} a \\ b \end{array} ") → D24
  30. LaTeX("x") → F24
  31. LaTeX("\begin{array}{} a \\ b \end{array} ") → D25
  32. LaTeX("x") → F25
  33. LaTeX("\begin{array}{} a \\ b \end{array} ") → D26
  34. LaTeX("x") → F26
  35. LaTeX("\begin{array}{} a \\ b \end{array} ") → D27
  36. LaTeX("x") → F27
  37. LaTeX("\begin{array}{} a \\ b \end{array} ") → D28
  38. LaTeX("x") → F28
  39. LaTeX("\begin{array}{} a \\ b \end{array} ") → D29
  40. LaTeX("x") → F29
  41. LaTeX("\begin{array}{} a \\ b \end{array} ") → D30
  42. LaTeX("x") → F30
  43. LaTeX("\begin{array}{} a \\ b \end{array} ") → D33
  44. LaTeX("x") → F33
  45. LaTeX("\begin{array}{} a \\ b \end{array} ") → D31
  46. LaTeX("x") → F31
  47. LaTeX("\begin{array}{} a \\ b \end{array} ") → D32
  48. LaTeX("x") → F32
  49. LaTeX("\begin{array}{} 3x-5y=-127 \\ 5x+y=-53 \end{array} ") → B18
  50. If(n ≟ 1, B18, If[n ≟ 2, D18, If[n ≟ 3, F18, ""]]) → A18
  51. LaTeX("\begin{array}{} x+5y=25 \\ 3x-y=43 \end{array} ") → B19
  52. If(n ≟ 1, B19, If[n ≟ 2, D19, If[n ≟ 3, F19, ""]]) → A19
  53. LaTeX("\begin{array}{} 3x-4y=45 \\ 3x+y=60 \end{array} ") → B20
  54. If(n ≟ 1, B20, If[n ≟ 2, D20, If[n ≟ 3, F20, ""]]) → A20
  55. LaTeX("\begin{array}{} 3x-3y=3 \\ -2x+y=5 \end{array} ") → B21
  56. If(n ≟ 1, B21, If[n ≟ 2, D21, If[n ≟ 3, F21, ""]]) → A21
  57. LaTeX("\begin{array}{} x+2y=-24 \\ 3x-y=54 \end{array} ") → B22
  58. If(n ≟ 1, B22, If[n ≟ 2, D22, If[n ≟ 3, F22, ""]]) → A22
  59. LaTeX("\begin{array}{} 3x-4y=-103 \\ 3x+y=-23 \end{array} ") → B23
  60. If(n ≟ 1, B23, If[n ≟ 2, D23, If[n ≟ 3, F23, ""]]) → A23
  61. LaTeX("\begin{array}{} a \\ b \end{array} ") → B24
  62. If(n ≟ 1, B24, If[n ≟ 2, D24, If[n ≟ 3, F24, ""]]) → A24
  63. LaTeX("\begin{array}{} a \\ b \end{array} ") → B25
  64. If(n ≟ 1, B25, If[n ≟ 2, D25, If[n ≟ 3, F25, ""]]) → A25
  65. LaTeX("\begin{array}{} a \\ b \end{array} ") → B26
  66. If(n ≟ 1, B26, If[n ≟ 2, D26, If[n ≟ 3, F26, ""]]) → A26
  67. LaTeX("\begin{array}{} a \\ b \end{array} ") → B27
  68. If(n ≟ 1, B27, If[n ≟ 2, D27, If[n ≟ 3, F27, ""]]) → A27
  69. LaTeX("\begin{array}{} a \\ b \end{array} ") → B28
  70. If(n ≟ 1, B28, If[n ≟ 2, D28, If[n ≟ 3, F28, ""]]) → A28
  71. LaTeX("\begin{array}{} a \\ b \end{array} ") → B29
  72. If(n ≟ 1, B29, If[n ≟ 2, D29, If[n ≟ 3, F29, ""]]) → A29
  73. LaTeX("\begin{array}{} a \\ b \end{array} ") → B30
  74. If(n ≟ 1, B30, If[n ≟ 2, D30, If[n ≟ 3, F30, ""]]) → A30
  75. LaTeX("\begin{array}{} a \\ b \end{array} ") → B31
  76. If(n ≟ 1, B31, If[n ≟ 2, D31, If[n ≟ 3, F31, ""]]) → A31
  77. LaTeX("\begin{array}{} a \\ b \end{array} ") → B32
  78. If(n ≟ 1, B32, If[n ≟ 2, D32, If[n ≟ 3, F32, ""]]) → A32
  79. LaTeX("\begin{array}{} a \\ b \end{array} ") → B33
  80. If(n ≟ 1, B33, If[n ≟ 2, D33, If[n ≟ 3, F33, ""]]) → A33
  81. Shuffle(lista1) → lista2
  82. If(A1 > 0, Element[lista2, 1], "") → B3
  83. If(A1 > 2, Element[lista2, 3], "") → B5
  84. If(A1 > 3, Element[lista2, 4], "") → B6
  85. If(A1 > 4, Element[lista2, 5], "") → B7
  86. If(A1 > 5, Element[lista2, 6], "") → B8
  87. If(A1 > 6, Element[lista2, 7], "") → B9
  88. If(A1 > 7, Element[lista2, 8], "") → B10
  89. If(A1 > 8, Element[lista2, 9], "") → B11
  90. If(A1 > 9, Element[lista2, 10], "") → B12
  91. If(A1 > 1, Element[lista2, 2], "") → B4
  92. If(A1 > 10, Element[lista2, 11], "") → F3
  93. If(A1 > 11, Element[lista2, 12], "") → F4
  94. If(A1 > 12, Element[lista2, 13], "") → F5
  95. If(A1 > 13, Element[lista2, 14], "") → F6
  96. If(A1 > 14, Element[lista2, 15], "") → F7
  97. If(A1 > 15, Element[lista2, 16], "") → F8
  98. If(A1 > 16, Element[lista2, 17], "") → F9
  99. If(A1 > 17, Element[lista2, 18], "") → F10
  100. If(A1 > 18, Element[lista2, 19], "") → F11
  101. If(A1 > 19, Element[lista2, 20], "") → F12
  102. TableText({{A3, B3}, {A4, B4}, {A5, B5}, {A6, B6}, {A7, B7}}, "|_") → texto1
  103. TableText({{A8, B8}, {A9, B9}, {A10, B10}, {A11, B11}, {A12, B12}}, "|_") → texto3