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Systems of Linear Inequalities Example

Systems of Linear Inequalities Example
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2017-01-16 03:15
Coordinate GeometryInequalityGeometric ConstructionGraphing
This example demonstrates how to graph the solution set of a system of linear inequalities in a coordinate plane, visually showing the regions that satisfy the conditions with different colors. Core math concepts include linear inequalities, boundary lines, solution regions, and algebraic operations. Construction highlights involve GeoGebra commands/objects like a, n_2, n_1, button1, n_3, b, c, button2, d, n_4, n_5, button3, e, i, j, text2, text4_1, text3_1, text1, text5_1, f, g, h, m_1, m_2, text3, A, B, used for defining inequalities, drawing lines, controlling parameters, and displaying text. Suitable for high school students learning linear programming and set operations, or for teacher demonstrations.

GeoGebra Commands & Parameters

  1. Numeric a(1)
  2. Numeric n_2(3)
  3. n_2 + a
  4. n_1 + n_2
  5. Numeric b(2)
  6. Numeric c(1)
  7. 0
  8. (b * n_1) + n_2
  9. (b * n_1) - n_2
  10. Boolean e(true)
  11. Boolean i(true)
  12. Boolean j(true)
  13. f(x, y) = y > (-x) + n_3
  14. g(x, y) = y > (b * x) - n_5
  15. h(x, y) = y < ((-b) * x) + n_4
  16. Numeric m_1(6)
  17. Numeric m_2(-3)
  18. (m_1, m_2)
  19. (m_1, m_2)

AI Drawing Prompt Reference

Draw a coordinate plane and show the solution set regions for two systems of linear inequalities. First, draw the line y > -x + 3, then draw the lines y > 2x - 1 and y < -2x + 6, using different colors to distinguish the regions that satisfy each inequality.
The prompt above was compiled from the original drawing commands and is for reference only.