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Solving Nonlinear Systems of Equations: 2 Variables by Roman Chijner

Solving Nonlinear Systems of Equations: 2 Variables by Roman Chijner
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2013-12-20 01:06
FunctionCoordinate GeometryGeometric Construction
In collections Solution of Systems of nonlinear Equations
This example demonstrates the graphical and numerical solution of a system of two nonlinear equations using GeoGebra's CAS feature. Key mathematical concepts include nonlinear equations, graphical solutions, and numerical methods. The construction involves commands such as Element, Point, If, Locus, Textfield, Polygon, Sequence, RemoveUndefined, Join, Text, Intersect, and Zip. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Element(lP, i) → P_i
  2. Point(Segment[Px2, Px1]) → Ax
  3. Point(Segment[Py2, Py1]) → Ay
  4. If(Funktion ≟ 1, a(x, y), If[Funktion ≟ 2, b(x, y), a(x, y) * b(x, y)]) → f00
  5. If((f1(x0 - ε / 2) * f1(x0 + ε / 2) < 1.0E-8) ∧ (f2(x0 - ε / 2) * f2(x0 + ε / 2) < 1.0E-8), (x0, y0)) → E0x
  6. If((g1(y0 - ε / 2) * g1(y0 + ε / 2) < 0) ∧ (g2(y0 - ε / 2) * g2(y0 + ε / 2) < 0), (x0, y0)) → E0y
  7. If(fxx(xi - ε / 2) * fxx(xi + ε / 2) < 0, (xi, y(Ay))) → Bxx1
  8. If(fyy(yi - ε / 2) * fyy(yi + ε / 2) < 0, (x(Ax), yi)) → Byy1
  9. Locus(Bxx1, Ay) → locxx1
  10. Locus(Byy1, Ax) → locyy1
  11. Textfield(a) → inputBox1
  12. Textfield(b) → inputBox2
  13. Polygon((x_{max}, y_{max}), (x_{min}, y_{max}), (x_{min}, y_{min}), (x_{max}, y_{min})) → VV, d, e, g, h
  14. Textfield(N_P) → Textfeld1
  15. If(a_1, N_P, 2) → N_1
  16. Sequence(x_{min} + (x_{max} - x_{min}) / N_1 * i, i, 0, N_1) → xx
  17. Sequence(y_{min} + (y_{max} - y_{min}) / N_1 * i, i, 0, N_1) → yy
  18. RemoveUndefined(Join[Zip[Mirror[{Roots[f00(a, x), y_{min}, y_{max}]}, y = x] + (a, 0), a, xx]]) → Pxxy
  19. Join(Zip[Reverse[{Roots[f00(x, b), x_{min}, x_{max}]}] + (0, b), b, yy]) → Pyyx
  20. Textfield(Funktion) → Textfeld2
  21. Textfield(x_{min}) → Textfeld3
  22. Textfield(y_{min}) → Textfeld4
  23. Textfield(x_{max}) → Textfeld5
  24. Textfield(y_{max}) → Textfeld6
  25. Textfield(N) → Textfeld7
  26. Text(Element[L, 1]) → Lx
  27. Text(Element[L, 2]) → Ly
  28. Intersect(Element[L, 1], Element[L, 2]) → C
  29. Zip((a(x(pp), y(pp)), b(x(pp), y(pp))), pp, lP) → Liste1
  30. Textfield(ε) → Textfeld8

AI Drawing Prompt Reference

Draw the graph of a system of two nonlinear equations by inputting two function expressions to find their intersection points. First, plot the graphs of the two functions, then use numerical methods to find the intersection points, and finally display the coordinates of the intersection points. Set the range of x and y values, as well as the number of points to refine the graph.
The prompt above was compiled from the original drawing commands and is for reference only.