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Solving Linear Equations via Transformations

Solving Linear Equations via Transformations
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2016-03-04 00:53
FunctionCoordinate GeometryTransformationGeometric Construction
This example demonstrates how to solve systems of linear equations visually using geometric transformations. Key math concepts include linear equations, transformations, and intersection points. It utilizes GeoGebra commands and objects such as Textfield, Intersect, Step, m_2, b_1, m_1, b_2, inputBoxm_1, inputBoxb_1, inputBoxm_2, inputBoxb_2, Transform_5, NoSolution, equalsX, AnyReal, Transform_1, Space, Comma, reset, Yzoom, Xzoom, Transform_3, Transform_2, trans5, Transform_4, trans1, trans3, trans2, trans4, f1, f2, fa, c, F1x, F1y, F1x_1, F1y_1, F2x, F2x_1, F2y, F2y_1, Fax. Suitable for high school mathematics teaching and self-learning, helping students understand the geometric meaning and solution steps of linear equation systems.

GeoGebra Commands & Parameters

  1. Textfield(m_1) → inputBoxm_1
  2. Textfield(b_1) → inputBoxb_1
  3. Textfield(m_2) → inputBoxm_2
  4. Textfield(b_2) → inputBoxb_2
  5. Intersect(f1, x = (0.7 * Xzoom), (14, 9)) → F1x
  6. Intersect(f1, y = (0.7 * Yzoom), (-1.2000000000000002, 1.4)) → F1y
  7. Intersect(f1, x = (-0.7 * Xzoom), (-14, -5)) → F1x_1
  8. Intersect(f1, y = (-0.7 * Yzoom), (-6.8, -1.4)) → F1y_1
  9. Intersect(f2, x = (0.7 * Xzoom), (14, -31)) → F2x
  10. Intersect(f2, x = (-0.7 * Xzoom), (-14, 25)) → F2x_1
  11. Intersect(f2, y = (0.7 * Yzoom), (-2.2, 1.4)) → F2y
  12. Intersect(f2, y = (-0.7 * Yzoom), (-0.8, -1.4)) → F2y_1
  13. Intersect(fa, x = (0.7 * Xzoom), (14, 9)) → Fax
  14. Intersect(fa, x = (-0.7 * Xzoom), (-14, -5)) → Fax_1
  15. Intersect(fa, y = (0.7 * Yzoom), (-1.2000000000000002, 1.4)) → Fay
  16. Intersect(fa, y = (-0.7 * Yzoom), (-6.8, -1.4)) → Fay_1