5.3 Graphical Solution (Two Variables)

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Solved Examples

  1. Boundary Line: Consider 3x+2y=63x + 2y = 6.
    • (x=0,y=3)(x=0, y=3) and (x=2,y=0)(x=2, y=0).
    • Draw a Dotted Line passing through (0,3)(0,3) and (2,0)(2,0) (since >> is strict).
  2. Test Point (0,0):
    • Substitute in 3x+2y>63x + 2y > 6:
    • 3(0)+2(0)>6  ⟹  0>63(0) + 2(0) > 6 \implies 0 > 6
    • FALSE.
  3. Shading: Since (0,0) is false, shade the half-plane away from the origin (Upper Right region).

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