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Solve System of Linear Inequalities in 2 Unknowns

Solve System of Linear Inequalities in 2 Unknowns
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2016-05-24 07:29
Coordinate GeometryInequalityGraphing
This example demonstrates how to graph and solve systems of linear inequalities in a 2D coordinate plane. Key math concepts include linear inequalities, region representation, and boundary lines. Construction highlights the use of GeoGebra commands and objects like RandomElement, If, Simplify, Line to generate random inequalities, draw lines, and display solution regions. Suitable for high school mathematics education to understand the geometric meaning of inequality solution sets.

GeoGebra Commands & Parameters

  1. RandomElement({1, 2, 3, 4}) → s4
  2. RandomElement({-4, -3, -2, -1, 1, 2, 3, 4}) → m3a
  3. RandomElement({1, 2, 3}) → m3b
  4. RandomElement({1, 2, 3} \ {m3b}) → m4b
  5. RandomElement({-4, -3, -2, -1, 0, 1, 2, 3, 4}) → x1
  6. RandomElement({1, 2, 3, 4}) → s1
  7. If(s1 ≟ 1, -1, 1) → k1
  8. RandomElement({x1 + k1, x1 + (k1 * 2), x1 + (k1 * 3), x1 + (k1 * 4)}) → x2
  9. RandomElement({-4, -3, -2, -1, 0, 1, 2, 3, 4}) → y1
  10. RandomElement({1, 2, 3, 4}) → s2
  11. If(s2 ≟ 1, -1, 1) → k2
  12. RandomElement({y1 + k2, y1 + (k2 * 2), y1 + (k2 * 3), y1 + (k2 * 4)}) → y2
  13. RandomElement({-4, -3, -2, -1, 1, 2, 3, 4}) → m4a
  14. If(s4 ≟ 1, (m4a * x) - (m4b * y) < (m4a * x2) - (m4b * y2), If[s4 ≟ 2, (m4a * x) - (m4b * y) ≤ (m4a * x2) - (m4b * y2), If[s4 ≟ 3, (m4a * x) - (m4b * y) > (m4a * x2) - (m4b * y2), (m4a * x) - (m4b * y) ≥ (m4a * x2) - (m4b * y2)]]) → h_1
  15. RandomElement({1, 2, 3, 4}) → s3
  16. If(s3 ≟ 1, (m3a * x) - (m3b * y) < (m3a * x2) - (m3b * y2), If[s3 ≟ 2, (m3a * x) - (m3b * y) ≤ (m3a * x2) - (m3b * y2), If[s3 ≟ 3, (m3a * x) - (m3b * y) > (m3a * x2) - (m3b * y2), (m3a * x) - (m3b * y) ≥ (m3a * x2) - (m3b * y2)]]) → g_1
  17. Simplify(g_1) → g
  18. Simplify(h_1) → h
  19. If(s1 ≟ 1, x < x1, If[s1 ≟ 2, x ≤ x1, If[s1 ≟ 3, x > x1, x ≥ x1]]) → e
  20. Line(A, B) → L1
  21. Line(C, D) → L2
  22. Line(E, F) → L3
  23. Line(G, H) → L4
  24. If(x(C) ≟ x(D), x > x(C), ((y - y(C)) * (x(C) - x(D))) - ((x - x(C)) * (y(C) - y(D))) > 0) → L2a
  25. If(x(C) ≟ x(D), x < x(C), ((y - y(C)) * (x(C) - x(D))) - ((x - x(C)) * (y(C) - y(D))) < 0) → L2b
  26. If(x(A) ≟ x(B), x > x(A), ((y - y(A)) * (x(A) - x(B))) - ((x - x(A)) * (y(A) - y(B))) > 0) → L1a
  27. If(x(A) ≟ x(B), x < x(A), ((y - y(A)) * (x(A) - x(B))) - ((x - x(A)) * (y(A) - y(B))) < 0) → L1b
  28. If(x(E) ≟ x(F), x > x(E), ((y - y(E)) * (x(E) - x(F))) - ((x - x(E)) * (y(E) - y(F))) > 0) → L3a
  29. If(x(E) ≟ x(F), x < x(E), ((y - y(E)) * (x(E) - x(F))) - ((x - x(E)) * (y(E) - y(F))) < 0) → L3b
  30. If(x(G) ≟ x(H), x > x(G), ((y - y(G)) * (x(G) - x(H))) - ((x - x(G)) * (y(G) - y(H))) > 0) → L4a
  31. If(x(G) ≟ x(H), x < x(G), ((y - y(G)) * (x(G) - x(H))) - ((x - x(G)) * (y(G) - y(H))) < 0) → L4b
  32. If(c1a ∧ c2a ∧ c3a ∧ c4a, L1a(x, y) ∧ L2a(x, y) ∧ L3a(x, y) ∧ L4a(x, y), If[c1a ∧ c2a ∧ c3a ∧ c4b, L1a(x, y) ∧ L2a(x, y) ∧ L3a(x, y) ∧ L4b(x, y), If[c1a ∧ c2a ∧ c3b ∧ c4a, L1a(x, y) ∧ L2a(x, y) ∧ L3b(x, y) ∧ L4a(x, y), If[c1a ∧ c2b ∧ c3a ∧ c4a, L1a(x, y) ∧ L2b(x, y) ∧ L3a(x, y) ∧ L4a(x, y), If[c1b ∧ c2a ∧ c3a ∧ c4a, L1b(x, y) ∧ L2a(x, y) ∧ L3a(x, y) ∧ L4a(x, y), If[c1b ∧ c2b ∧ c3a ∧ c4a, L1b(x, y) ∧ L2b(x, y) ∧ L3a(x, y) ∧ L4a(x, y), If[c1b ∧ c2a ∧ c3b ∧ c4a, L1b(x, y) ∧ L2a(x, y) ∧ L3b(x, y) ∧ L4a(x, y), If[c1b ∧ c2a ∧ c3a ∧ c4b, L1b(x, y) ∧ L2a(x, y) ∧ L3a(x, y) ∧ L4b(x, y), If[c1a ∧ c2b ∧ c3b ∧ c4a, L1a(x, y) ∧ L2b(x, y) ∧ L3b(x, y) ∧ L4a(x, y), If[c1a ∧ c2b ∧ c3a ∧ c4b, L1a(x, y) ∧ L2b(x, y) ∧ L3a(x, y) ∧ L4b(x, y), If[c1a ∧ c2a ∧ c3b ∧ c4b, L1a(x, y) ∧ L2a(x, y) ∧ L3b(x, y) ∧ L4b(x, y), If[c1b ∧ c2b ∧ c3b ∧ c4a, L1b(x, y) ∧ L2b(x, y) ∧ L3b(x, y) ∧ L4a(x, y), If[c1b ∧ c2b ∧ c3a ∧ c4b, L1b(x, y) ∧ L2b(x, y) ∧ L3a(x, y) ∧ L4b(x, y), If[c1b ∧ c2a ∧ c3b ∧ c4b, L1b(x, y) ∧ L2a(x, y) ∧ L3b(x, y) ∧ L4b(x, y), If[c1a ∧ c2b ∧ c3b ∧ c4b, L1a(x, y) ∧ L2b(x, y) ∧ L3b(x, y) ∧ L4b(x, y), If[c1b ∧ c2b ∧ c3b ∧ c4b, L1b(x, y) ∧ L2b(x, y) ∧ L3b(x, y) ∧ L4b(x, y)]]]]]]]]]]]]]]]) → checkSol
  33. Simplify((m3a * (x - x2)) + (y2 * m3b)) → g_2
  34. Simplify((m4a * (x - x2)) + (y2 * m4b)) → h_2
  35. If(s2 ≟ 1, (0 * x) + y < y1, If[s2 ≟ 2, (0 * x) + y ≤ y1, If[s2 ≟ 3, (0 * x) + y > y1, (0 * x) + y ≥ y1]]) → f_1
  36. Simplify(f_1) → f
  37. Line(A, B) → L1solid
  38. Line(C, D) → L2solid
  39. Line(E, F) → L3solid
  40. Line(G, H) → L4solid
  41. If(caly ≟ 3, y2 + (m3a / m3b * (tempx - x2)), If[caly ≟ 4, y2 + (m4a / m4b * (tempx - x2))]) → tempy