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Solving Nonlinear Systems of Equations: 2 Variables

Solving Nonlinear Systems of Equations: 2 Variables
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2014-07-13 00:04
FunctionCoordinate GeometryCalculus
In collections Solution of Systems of nonlinear Equations
This example demonstrates the graphical and numerical solution of a system of two nonlinear equations. It involves key mathematical concepts such as solving nonlinear equations, coordinate geometry, and numerical computation. Using GeoGebra commands like Element, Point, If, Textfield, etc., a dynamic graphical representation of the solution to the nonlinear system is constructed. 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. Textfield(a) → inputBox1
  8. Textfield(b) → inputBox2
  9. Polygon((x_{max}, y_{max}), (x_{min}, y_{max}), (x_{min}, y_{min}), (x_{max}, y_{min})) → VV, d, e, g, h
  10. Textfield(N_P) → Textfeld1
  11. If(a_1, N_P, 2) → N_1
  12. Sequence(x_{min} + ((x_{max} - x_{min}) / N_1 * i), i, 0, N_1) → xx
  13. Sequence(y_{min} + ((y_{max} - y_{min}) / N_1 * i), i, 0, N_1) → yy
  14. RemoveUndefined(Join[Zip[Mirror[{Roots[f00(a, x), y_{min}, y_{max}]}, y = x] + (a, 0), a, xx]]) → Pxxy
  15. Join(Zip[Reverse[{Roots[f00(x, b), x_{min}, x_{max}]}] + (0, b), b, yy]) → Pyyx
  16. Textfield(Funktion) → Textfeld2
  17. Textfield(x_{min}) → Textfeld3
  18. Textfield(y_{min}) → Textfeld4
  19. Textfield(x_{max}) → Textfeld5
  20. Textfield(y_{max}) → Textfeld6
  21. Text(Element[L, 1]) → Lx
  22. Text(Element[L, 2]) → Ly
  23. Intersect(Element[L, 1], Element[L, 2]) → C
  24. Zip((a(x(pp), y(pp)), b(x(pp), y(pp))), pp, lP) → Liste1

AI Drawing Prompt Reference

Draw the graph of a system of two nonlinear equations, input the two equations, set the minimum and maximum values for x and y, generate the corresponding function graphs, find the intersection points, and display the coordinates of the intersection points.
The prompt above was compiled from the original drawing commands and is for reference only.