SISTEMA DE INECUACIONES

CON DOS VARIABLES

A. x + y ≥ -1X + y < 2

X + y = -1 x = 0 ; y = -1 (0 ; -1) x = -1 ; y = 0 (-1 ; 0)

X + y = -1X + y = 2

X + y = 2 x = 0 ; y = 2 (0 ; 4) x = 2 ; y = 0 (2 ; 0)

.. ..X + y ≥ -1X = 0 => 0 + 0 ≥ -1 Y = 0 0 ≥ -1……(V)

X + y < 2X = 0 => 0 + 0 < 2 Y = 0 0 ≥ 2……(V)

B. X + y ≤ 43x + y ≤ 6

X + y = 4 x = 0 ; y = 4 (0 ; 4) x = 4 ; y = 0 (4 ; 0)

X + y = 43X + y = 6

3X + y = 6 x = 0 ; y = 6 (0 ; 6) x = 2 ; y = 0 (6 ; 0)

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.X + y ≤ 4X = 0 => 0 + 0 ≤ 4 Y = 0 0 ≤ 4……(V)

3X + y ≤ 6X = 0 => 3(0) + 0 ≤ 6 Y = 0 0 ≤ 6……(V)

C. X + y ≥ 2x + y ≤ 5X ≥ 0Y ≥ 0

X + y = 2 x = 0 ; y = 2 (0 ; 2) x = 2 ; y = 0 (2 ; 0)

X + y = 2X + y = 5X = 0Y = 0

X + y = 5 x = 0 ; y = 5 (0 ; 5) x = 5 ; y = 0 (5 ; 0)

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X + y ≥ 2X = 0 => 0 + 0 ≥ 2 Y = 0 0 ≥ 2……(F)

X + y ≤ 5X = 0 => 0 + 0 ≤ 5 Y = 0 0 ≤ 5……(V)

D. y - x ≤ 1y – 2x ≤ -3X ≥ 0Y ≥ 0

y - x = 1 x = 0 ; y = 1 (0 ; 1) x = 1 ; y = 2 (1 ; 2)

y - x = 1y – 2x = -3X = 0Y = 0

Y – 2x = -3 x = 0 ; y = -3 (0 ; -3) x = 2 ; y = 1 (2 ; 1)

.Y – x ≤ 1X = 0 => 0 - 0 ≤ 1 Y = 0 0 ≤ 1……(V)

X - 2y ≤ -3X = 0 => 0 – 2(0) ≤ -3 Y = 0 0 ≤ -3……(F)

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E. X + 2y ≤ 20x ≤ 10X ≥ 0Y ≥ 0

X + 2y = 20 x = 20 ; y = 0 (20 ; 0) x = 0 ; y = 10 (0 ; 10)

X + 2y = 20X = 10X = 0Y = 0

X + 2y ≤ 20X = 0 => 0 + 2(0) ≤ 20 Y = 0 0 ≤ 20……(V)

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F. y ≤ 3x + 1y ≤ -4x + 16y ≥ 0Y ≤ 4X ≥ 0

y = 3x + 1 x = 0 ; y = 1 (0 ; 1) x = 1 ; y = 4 (1 ; 4)

y = 3x + 1y = -4x + 16y = 0Y = 4X = 0

y = -4x + 16 x = 2 ; y = 8 (2 ; 8) x = 3 ; y = 4 (3 ; 4)

y ≤ 3x + 1X = 0 => 0 ≤ 3(0) + 1Y = 0 0 ≤ 1……(V)

y ≤ -4x + 16 X = 0 => 0 ≤ -4(0) + 16Y = 0 0 ≤ 16……(V)

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G. X – y ≥ 32x + y < 4

X – y = 3 x = 0 ; y = -3 (0 ; -3) x = 3 ; y = 0 (3 ; 0)

2x + y = 4 x = 0 ; y = 4 (0 ; 4) x = 2 ; y = 0 (2 ; 0)

X – y ≥ 3X = 0 => 0 – 0 ≥ 3Y = 0 0 ≥ 3……(F)

2x + y < 4X = 0 => 2(0) + 0 < 4Y = 0 0 ≤ 4……(V)

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X – y = 32x + y = 4