Question

Resolver el siguiente Sistema de ecuaciones y compruebe su solución:

3x+2y-z=2
x-4y+2z=1
2x-3z=4

Answer 1

metodo de sustitucion
3x+2y-x=2
x-4y+2z=1
2x-3z=4

3 x+2 y-z = 2
x-4 y+2 z = 1
2 x-3 z = 4

3 x+2 y-z = 2
x = 1+4 y-2 z
2 x-3 z = 4

2 y+3 (1+4 y-2 z)-z = 2
x = 1+4 y-2 z
2 (1+4 y-2 z)-3 z = 4
2 y+3 (1+4 y-2 z)-z = 2 y+(3+12 y-6 z)-z = 3+14 y-7 z:

3+14 y-7 z = 2
x = 1+4 y-2 z
2 (1+4 y-2 z)-3 z = 4
2 (1+4 y-2 z)-3 z = (2+8 y-4 z)-3 z = 2+8 y-7 z:

3+14 y-7 z = 2
x = 1+4 y-2 z
2+8 y-7 z = 4

3+14 y-7 z = 2
x = 1+4 y-2 z
2+8 y-7 z = 4

14 y = 7 z-1
x = 1+4 y-2 z
2+8 y-7 z = 4

y = z/2-1/14
x = 1+4 y-2 z
2+8 y-7 z = 4 

y = z/2-1/14
x = 1+4 y-2 z
2+8 (z/2-1/14)-7 z = 4
2+8 (z/2-1/14)-7 z = (4 z-4/7)-7 z+2 = 10/7-3 z:

y = z/2-1/14
x = 1+4 y-2 z
10/7-3 z = 4

y = z/2-1/14
x = 1+4 y-2 z
10/7-3 z = 4

y = z/2-1/14
x = 1+4 y-2 z
-3 z = 18/7

y = z/2-1/14
x = 1+4 y-2 z
z = -6/7

y = (-1)/2
x = 4 y+19/7
z = -6/7

y = -1/2
x = 5/7
z = -6/7

x = 5/7
y = -1/2
z = -6/7
:)