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Example of Linear Inequality System

Example of Linear Inequality System
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2020-09-09 00:08
Coordinate GeometryInequalityGeometric Construction
In collections PROGRAM LINEAR
This example demonstrates the graphical representation of a system of linear inequalities. Key mathematical concepts include linear inequalities, boundary lines, and shaded regions. Using GeoGebra commands such as a, b, c, d, etc., the system of inequalities is constructed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. a(x, y) = x + y ≤ 6
  2. b(x, y) = x + (2 * y) ≤ 8
  3. c: x ≥ 0
  4. d: y ≥ 0
  5. Boolean e(false)
  6. Boolean f(false)
  7. Boolean g(false)
  8. Boolean h(false)
  9. i(x, y) = a(x, y) ∧ b(x, y)
  10. i_1(x, y) = a(x, y) ∧ b(x, y)
  11. j(x, y) = a(x, y) ∧ c(x)
  12. j_1(x, y) = a(x, y) ∧ c(x)
  13. k(x, y) = a(x, y) ∧ d(y)
  14. k_1(x, y) = a(x, y) ∧ d(y)
  15. l(x, y) = b(x, y) ∧ c(x)
  16. l_1(x, y) = b(x, y) ∧ c(x)
  17. m(x, y) = b(x, y) ∧ d(y)
  18. m_1(x, y) = b(x, y) ∧ d(y)
  19. n(x, y) = c(x) ∧ d(y)
  20. n_1(x, y) = c(x) ∧ d(y)
  21. o(x, y) = a(x, y) ∧ b(x, y) ∧ c(x)
  22. p(x, y) = a(x, y) ∧ b(x, y) ∧ d(y)
  23. q(x, y) = a(x, y) ∧ c(x) ∧ d(y)
  24. r(x, y) = b(x, y) ∧ c(x) ∧ d(y)
  25. o_1(x, y) = a(x, y) ∧ b(x, y) ∧ c(x)
  26. o_2(x, y) = a(x, y) ∧ b(x, y) ∧ c(x)
  27. p_1(x, y) = a(x, y) ∧ b(x, y) ∧ d(y)
  28. p_2(x, y) = a(x, y) ∧ b(x, y) ∧ d(y)
  29. q_1(x, y) = a(x, y) ∧ c(x) ∧ d(y)
  30. q_2(x, y) = a(x, y) ∧ c(x) ∧ d(y)
  31. r_1(x, y) = b(x, y) ∧ c(x) ∧ d(y)
  32. r_2(x, y) = b(x, y) ∧ c(x) ∧ d(y)
  33. s(x, y) = a(x, y) ∧ b(x, y) ∧ c(x) ∧ d(y)
  34. s_4(x, y) = a(x, y) ∧ b(x, y) ∧ c(x) ∧ d(y)
  35. s_3(x, y) = a(x, y) ∧ b(x, y) ∧ c(x) ∧ d(y)
  36. s_2(x, y) = a(x, y) ∧ b(x, y) ∧ c(x) ∧ d(y)
  37. x = 0
  38. y = 0
  39. x + y = 6
  40. x + (2 * y) = 8