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Solving Simultaneous Linear Inequalities II (Self Directed Practice)

Solving Simultaneous Linear Inequalities II (Self Directed Practice)
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2020-03-29 17:46
Coordinate GeometryInequalityGeometric Construction
This example demonstrates how to graph and solve simultaneous linear inequalities in GeoGebra, visually representing the solution regions. Core math concepts include inequalities, linear equations, and region representation. Key GeoGebra commands used are Solve, Segment, Polygon, Min, Max, etc., making it suitable for high school mathematics practice and self-directed learning.

GeoGebra Commands & Parameters

  1. TextToUnicode(Text[c_1]) → lc_1
  2. Sequence(If[Defined[IndexOf[Element[listIneqsym_1, n], lc_1]], IndexOf[Element[listIneqsym_1, n], lc_1], 0], n, 1, 4) → clsr1_1
  3. If(Length[clsr1_1] - Sum[Sequence[If[Element[clsr1_1, t] ≟ 0, 1, 0], t, 1, 4]] < 2, Sequence[If[Defined[IndexOf[Element[listIneqsym_1, n], lc_1, Sum[clsr1_1] + 1]], IndexOf[Element[listIneqsym_1, n], lc_1, Sum[clsr1_1] + 1], 0], n, 1, 4], {0, 0, 0, 0}) → clsr2_1
  4. Element({f1(x) < f0(x), f1(x) ≤ f0(x), f1(x) > f0(x), f1(x) ≥ f0(x)}, counttb1) → ineq1
  5. Textfield(txtInputf1) → InputBox1
  6. Textfield(txtInputg1) → InputBox2
  7. Textfield(txtInputf0) → InputBox3
  8. Text(Element[listtb1Ineq, counttb1]) → txtboxlistIneq1
  9. Text(Element[listtb2Ineq, counttb2]) → txtboxlistIneq2
  10. Element({f0(x) < g1(x), f0(x) ≤ g1(x), f0(x) > g1(x), f0(x) ≥ g1(x)}, counttb2) → ineq2
  11. Solve(ineq2) → ineq2solved
  12. Solve(ineq1) → ineq1solved
  13. Element(ineq2solved, 1) → a_2
  14. Element(ineq1solved, 1) → a_1
  15. Text(UnicodeToText[Last[TextToUnicode[Text[a_1]], Length[TextToUnicode[Text[a_1]]] - 3]]) → txtIneq1numpivot
  16. Text(UnicodeToText[Last[TextToUnicode[Text[a_2]], Length[TextToUnicode[Text[a_2]]] - 3]]) → txtIneq2numpivot
  17. LaTeX(If[Length[Text[$3]] < 3, "\text{There is no solution}", LaTeX[UnicodeToText[Remove[TextToUnicode[Text[$3]], {123, 125}]]]], false) → txteq1and2solvedalt
  18. LaTeX(UnicodeToText[Remove[TextToUnicode[Text[$1]], {123, 125}]]) → txtSolveineq1
  19. Reverse(TextToUnicode[txteq1and2solvedalt]) → l1
  20. TextToUnicode(txteq1and2solvedalt) → l2
  21. TextToUnicode(Text[a_3]) → la_1
  22. TextToUnicode(Text[b_3]) → lb_1
  23. Sequence(Point[a_3, t] + (0, shiftA_1), t, 0, 1) → Endpointsa_1
  24. Sequence(Point[b_3, t] + (0, shiftB_1), t, 0, 1) → Endpointsb_1
  25. Sequence(Sequence[Element[{clsr1_1, clsr2_1}, n, m], m, 1, 4], n, 1, 2) → cls_1, {{9, 0, 5, 0}, {0, 0, 0, 0}}
  26. Sequence(Point[c_1, t] + (0, shiftC_1), t, 0, 1) → Endpointsc_1
  27. Sequence(Sequence[If[Defined[IndexOf[Element[listIneqsym_1, CLIPBOARDmagicSTRINGt], lb_1, n]], IndexOf[Element[listIneqsym_1, CLIPBOARDmagicSTRINGt], lb_1, n], 0], CLIPBOARDmagicSTRINGt, 1, 4], n, 1, 4, 3) → bls_1, {{0, 0, 0, 3}, {0, 0, 0, 0}}
  28. Sequence(Sequence[If[Defined[IndexOf[Element[listIneqsym_1, CLIPBOARDmagicSTRINGt], la_1, n]], IndexOf[Element[listIneqsym_1, CLIPBOARDmagicSTRINGt], la_1, n], 0], CLIPBOARDmagicSTRINGt, 1, 4], n, 1, 4, 3) → als_1, {{3, 0, 0, 0}, {0, 0, 0, 0}}
  29. Sequence(If[Element[cls_1, 1, m] + Element[cls_1, 2, m] ≟ 0, 0, If[Element[cls_1, 1, m] ≟ Element[cls_1, 2, m], 1, If[(Element[cls_1, 1, m] * Element[cls_1, 2, m]) ≟ 0, 1, 2]]], m, 1, 4) → clls_1
  30. Sequence(If[Element[bls_1, 1, m] + Element[bls_1, 2, m] ≟ 0, 0, If[Element[bls_1, 1, m] ≟ Element[bls_1, 2, m], 1, If[(Element[bls_1, 1, m] * Element[bls_1, 2, m]) ≟ 0, 1, 2]]], m, 1, 4) → blls_1
  31. Sequence(If[Element[als_1, 1, m] + Element[als_1, 2, m] ≟ 0, 0, If[Element[als_1, 1, m] ≟ Element[als_1, 2, m], 1, If[(Element[als_1, 1, m] * Element[als_1, 2, m]) ≟ 0, 1, 2]]], m, 1, 4) → alls_1
  32. If(IndexOf[1, alls_1] > 2, 0, 2) → pta_1
  33. If(IndexOf[1, blls_1] > 2, 0, 2) → ptb_1
  34. If(IndexOf[1, alls_1] ≟ 1 ∨ IndexOf[1, alls_1] ≟ 3, 2, 1) → da_1
  35. If(IndexOf[1, blls_1] ≟ 1 ∨ IndexOf[1, blls_1] ≟ 3, 2, 1) → db_1
  36. Element(Endpointsa_1, da_1) → sta_1
  37. Element(Endpointsb_1, db_1) → stb_1
  38. Element(Endpointsa_1, If[da_1 ≟ 1, 2, 1]) → eta_1
  39. Element(Endpointsb_1, If[db_1 ≟ 1, 2, 1]) → etb_1
  40. Segment(sta_1, eta_1) → sega_1
  41. Segment(stb_1, etb_1) → segb_1
  42. Element(Endpointsc_1, 1) → stc1_1
  43. Element(Endpointsc_1, 2) → stc2_1
  44. If(c_1(stc2_1), 0, 2) → ptc2_1
  45. If(c_1(stc1_1), 0, 2) → ptc1_1
  46. If(Sum[clls_1] ≟ 1, If[IndexOf[1, clls_1] ≟ 1 ∨ IndexOf[1, clls_1] ≟ 3, 2, 1], 3) → flagc_1
  47. Polygon(stc1_1, stc2_1, (x(stc2_1), 0), (x(stc1_1), 0)) → soln_1, f_1, g_1, h_1, i_1
  48. If(flagc_1 ≟ 2, Segment[stc2_1, stc1_1], Segment[stc1_1, stc2_1]) → segc_1
  49. Min(Max[{x(Element[Endpointsa_1, 1]), x(Element[Endpointsa_1, 2]), x(Element[Endpointsb_1, 1]), x(Element[Endpointsb_1, 2]), x(Element[Endpointsc_1, 1]), x(Element[Endpointsc_1, 2])}] + 1.5, 25) → xmax
  50. Max(Min[{x(Element[Endpointsa_1, 1]), x(Element[Endpointsa_1, 2]), x(Element[Endpointsb_1, 1]), x(Element[Endpointsb_1, 2]), x(Element[Endpointsc_1, 1]), x(Element[Endpointsc_1, 2])}] - 1.5, -20) → xmin
  51. Defined(a_1) → ineqdefinedf
  52. Defined(a_2) → ineqdefinedg