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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)
..
.
.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)
. . .
.
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)
. .
.
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)
.. .
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)
....
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)
..
..
X – y = 32x + y = 4