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Practice: Solving Simultaneous Equations with Three Unknowns (Level 2)

Practice: Solving Simultaneous Equations with Three Unknowns (Level 2)
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2015-12-10 16:08
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This GeoGebra example demonstrates solving a system of three linear equations in three unknowns using determinants. It randomly generates coefficients and constants, allowing students to input solutions and receive immediate feedback via text fields. The core mathematical concepts include determinant computation, Cramer's rule, and the conditions for solution existence. The construction uses GeoGebra commands such as Random, Determinant, Textfield, Segment, and If, and defines numerous objects to store intermediate results and answers. It is suitable for high school or early university linear algebra courses as a practice activity.

GeoGebra Commands & Parameters

  1. Random(-20, 20) → ans_1
  2. Random(-9, 9) → b
  3. Random(-20, 20) → ans_3
  4. Random(-9, 9) → e
  5. Random(-20, 20) → ans_2
  6. Random(-9, 9) → f
  7. Random(-9, 9) → h
  8. Random(-9, 9) → c
  9. Random(-9, 9) → g
  10. Random(-9, 9) → i
  11. Random(-9, 9) → d
  12. Random(-9, 9) → a
  13. Determinant(q) → i_1
  14. Determinant(r) → j
  15. Determinant(s) → k
  16. Determinant(w) → w_1
  17. Textfield(abc) → InputBox1
  18. Textfield(abd) → InputBox2
  19. Textfield(abe) → InputBox3
  20. Textfield(abf) → InputBox4
  21. Textfield(abi) → InputBox8
  22. Textfield(abk) → InputBox9
  23. Textfield(abj) → InputBox10
  24. Textfield(abl) → InputBox11
  25. Textfield(ansy) → InputBox12
  26. Textfield(ansz) → InputBox13
  27. Textfield(ansx) → InputBox7
  28. Textfield(abh) → InputBox5
  29. Textfield(abg) → InputBox6
  30. Segment(A, B) → a_1
  31. Segment(C, D) → b_1
  32. Segment(E, F) → c_1
  33. Segment(E, F) → d_1
  34. If(ansx ≟ mx ∧ ansy ≟ nx ∧ ansz ≟ wx, "Well Done!", "Please Try Again") → text24