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Basic Systems of Equations Example

Basic Systems of Equations Example
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2021-06-13 20:39
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This example demonstrates the graphical solution of basic linear systems of equations, visually showing the intersection points of geometric graphs. Core math concepts include linear equations, geometric intersections, and analytical geometry. Construction highlights GeoGebra commands/objects like RandomElement, If, RandomDiscrete, Textfield, FractionText, and objects such as List1, A_{s2}, B_{s2}. Suitable for high school mathematics teaching to help students understand the solutions of linear systems and their geometric interpretations.

GeoGebra Commands & Parameters

  1. RandomElement(List1a) → D_{s2}
  2. If(B_{s2} / D_{s2} ≟ A_{s2}, (-D_{s2}), D_{s2}) → D_{s}
  3. RandomElement(List1a) → C_{s1}
  4. RandomElement(List1a) → B_{s1}
  5. RandomElement(List1a) → A_{s1}
  6. If(A_{s1} / C_{s1} ≟ B_{s1}, (-C_{s1}), C_{s1}) → C_{s}
  7. RandomDiscrete({1, 2, 3, 4, 5, 6, 7}, {10, 4, 3, 2, 1, 0, 2}) → a
  8. RandomDiscrete({1, 2, 3, 4, 5, 6, 7}, {10, 3, 3, 2, 1, 0, 2}) → b_{1}
  9. If(b_{1} ≟ 7 ∧ a ≟ 7, 1, b_{1}) → b
  10. If(a ≟ 1, RandomElement[List1], a ≟ 6, RandomElement[List6], RandomElement[List7], a ≟ 2, RandomElement[List2], a ≟ 3, RandomElement[List3], a ≟ 4, RandomElement[List4], a ≟ 5, RandomElement[List5]) → m_{e}
  11. If(b ≟ 1, RandomElement[List1], b ≟ 6, RandomElement[List6], RandomElement[List7], b ≟ 2, RandomElement[List2], b ≟ 3, RandomElement[List3], b ≟ 4, RandomElement[List4], b ≟ 5, RandomElement[List5]) → n_{e}
  12. If(a ≟ 1, RandomElement[List1a], a ≟ 6, RandomElement[List6a], RandomElement[List7a], a ≟ 2, RandomElement[List2a], a ≟ 3, RandomElement[List3a], a ≟ 4, RandomElement[List4a], a ≟ 5, RandomElement[List5a]) → A_{e}
  13. If(a ≟ 1, RandomElement[List1a], a ≟ 6, RandomElement[List6a], RandomElement[List7a], a ≟ 2, RandomElement[List2a], a ≟ 3, RandomElement[List3a], a ≟ 4, RandomElement[List4a], a ≟ 5, RandomElement[List5a]) → C_{e}
  14. If(b ≟ 1, RandomElement[List1a], b ≟ 6, RandomElement[List6a], RandomElement[List7a], b ≟ 2, RandomElement[List2a], b ≟ 3, RandomElement[List3a], b ≟ 4, RandomElement[List4a], b ≟ 5, RandomElement[List5a]) → B_{e}
  15. If(b ≟ 1, RandomElement[List1a], b ≟ 6, RandomElement[List6a], RandomElement[List7a], b ≟ 2, RandomElement[List2a], b ≟ 3, RandomElement[List3a], b ≟ 4, RandomElement[List4a], b ≟ 5, RandomElement[List5a]) → D_{1}
  16. If(A_{e} / C_{e} ≟ B_{e} / D_{1}, (-D_{1}), D_{1}) → D_{e}
  17. RandomDiscrete({1, -1, 2, -2, 3, -3, 4, -4, 5, -5, 6, -6, 7, -7, 8, -8, 9, -9, 10, -10, 0}, {8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 6}) → m_{s}
  18. RandomDiscrete({1, -1, 2, -2, 3, -3, 4, -4, 5, -5, 6, -6, 7, -7, 8, -8, 9, -9, 10, -10, 0}, {8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 6}) → n_{s}
  19. RandomElement({2, 3, 4, 5, 6, -2, -3, -4, -5, -6}) → howmuchbigger
  20. If(Choice ≟ 1, ((-C_{s}) * howmuchbigger), Choice ≟ 2, (C_{s} * howmuchbigger), Choice ≟ 3, howmuchbigger, Choice ≟ 4, howmuchbigger, Choice ≟ 5, (A_{e} * howmuchbigger)) → A_{big}
  21. If(Choice ≟ 1, howmuchbigger, Choice ≟ 2, howmuchbigger, Choice ≟ 3, ((-D_{s}) * howmuchbigger), Choice ≟ 4, (D_{s} * howmuchbigger), Choice ≟ 5, (B_{e} * howmuchbigger)) → B_{big}
  22. If(Choice ≟ 1, (D_{s1} * howmuchbigger) + RandomElement[List1], Choice ≟ 2, (D_{s1} * howmuchbigger) + RandomElement[List1], Choice ≟ 3, (C_{s2} * howmuchbigger) + RandomElement[List1], Choice ≟ 4, (C_{s2} * howmuchbigger) + RandomElement[List1], Choice ≟ 5, (R_{e} * howmuchbigger) + RandomElement[List1]) → nosolution
  23. If(Choice ≟ 1, (D_{s1} * howmuchbigger), Choice ≟ 2, (D_{s1} * howmuchbigger), Choice ≟ 3, (C_{s2} * howmuchbigger), Choice ≟ 4, (C_{s2} * howmuchbigger), Choice ≟ 5, (R_{e} * howmuchbigger)) → infsolutions
  24. If(Choice ≟ 1, m_{s}, Choice ≟ 2, m_{s}, Choice ≟ 3, m_{s}, Choice ≟ 4, m_{s}, Choice ≟ 5, m_{e}) → x_{ans1}
  25. If(Choice ≟ 1, n_{s}, Choice ≟ 2, n_{s}, Choice ≟ 3, n_{s}, Choice ≟ 4, n_{s}, Choice ≟ 5, n_{e}) → y_{ans1}
  26. If(answercode ≟ 1, x_{ans1}, answercode ≟ 2, -1000, answercode ≟ 3, 1000) → x_{ans}
  27. If(answercode ≟ 1, y_{ans1}, answercode ≟ 2, -1000, answercode ≟ 3, 1000) → y_{ans}
  28. Textfield(x_{guess}) → InputBox1
  29. Textfield(y_{guess}) → InputBox2
  30. FractionText((x_{ans}, y_{ans})) → fractext

AI Drawing Prompt Reference

Draw a graph containing two straight lines that intersect at a single point. The lines should be clearly drawn, and the intersection point should be marked. Text labels can be added near the intersection to display the coordinates. The overall composition should be clear and simple to help understand the geometric solution of linear systems.
The prompt above was compiled from the original drawing commands and is for reference only.