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使用代入法解线性方程组

使用代入法解线性方程组
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2019-04-12 21:10
函数解析几何不等式
①本范例演示使用代入法解线性方程组的数学过程；②涉及的核心数学概念为线性方程组、代入法、解析几何；③作图要点提炼自构造摘要，使用了Element, UnicodeToText, Polygon, LaTeX, Textfield, UnicodeToLetter, If等GeoGebra命令/对象；④适合初中及以上数学学习者，用于理解和练习线性方程组的解法。

GeoGebra 命令及参数

  1. Element(questionList, questionListIndex) → questionNum
  2. Element(D2:D9, questionNum) → correctLHS
  3. Element(E2:E9, questionNum) → correctRHS1
  4. Element(F2:F9, questionNum) → correctRHS2
  5. UnicodeToText(TextToUnicode[userLHS] \ {32}) → userLHSnoSpace
  6. UnicodeToText(TextToUnicode[userRHS] \ {32}) → userRHSnoSpace
  7. Element(K2:K9, questionNum) → correctSub
  8. Element(C2:C9, questionNum) → equationToIsolate
  9. Polygon({(-11, -11), (-11, 11), (11, 11), (11, -11)}) → viewBox
  10. LaTeX((((("\text{" * QUESTION) * "\\") * INSTRUCTIONS) * "}")) → TEXT
  11. Element(A2:A9, questionNum) → equation1
  12. Element(B2:B9, questionNum) → equation2
  13. Textfield(userLHS) → ansLHS
  14. Textfield(userRHS) → ansRHS
  15. LaTeX("=") → equalSign
  16. LaTeX("\text{Step 3: Select the correct substitution of the variable isolated in Step 2.}") → step3Instructions
  17. LaTeX("\text{Step 2: Isolate the most appropriate variable in the equation chosen in Step 1.}") → step2Instructions
  18. LaTeX(Element[G2:G9, questionNum]) → labelSubOption1
  19. LaTeX(Element[H2:H9, questionNum]) → labelSubOption2
  20. LaTeX(Element[I2:I9, questionNum]) → labelSubOption3
  21. LaTeX(Element[J2:J9, questionNum]) → labelSubOption4
  22. LaTeX("\fcolorbox{black}{#fff59d}{\text{Look for an equation that has a variable with\\a coefficient of \(1\).}}") → feedbackStep1
  23. UnicodeToLetter(10003) → cmarkStep1
  24. If(Take[userRHSnoSpace, 1, 1] ≟ "-", userRHSnoSpace, "+" + userRHSnoSpace) → userRHSwithPlus
  25. LaTeX("\fcolorbox{black}{#fff59d}{\text{Substitute the isolated variable into the equation not\\chosen in Step 1. Remember that the operation between\\a variable and its coefficient is multiplication.}}") → feedbackStep3
  26. LaTeX(equation1) → labelEquation1
  27. LaTeX(equation2) → labelEquation2
  28. UnicodeToLetter(10003) → cmarkStep2
  29. LaTeX("\text{Step 1: Select the equation that is best set up for isolating a variable.}") → step1Instructions
  30. LaTeX((((("\fcolorbox{black}{#fff59d}{\text{Rearrange the equation so that a variable with a coefficient of\\\(1\) is isolated on the left. In this instance, \(" * correctLHS) * "=") * correctRHS1) * "\).}}")) → feedbackStep2