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Solving a Linear System by Substitution

Solving a Linear System by Substitution
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2019-04-12 21:10
FunctionCoordinate GeometryInequality
This example demonstrates the process of solving a linear system using the substitution method. Key math concepts include linear equations, substitution method, and coordinate geometry. It utilizes GeoGebra commands/objects like Element, UnicodeToText, Polygon, LaTeX, Textfield, UnicodeToLetter, If as outlined in the construction summary. Suitable for middle school and above students for understanding and practicing solving linear systems.

GeoGebra Commands & Parameters

  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