Question

x+2y+z=9 2x+y-z=3 3x-y-2z=-4

Answer 1

x + 2y + z = 9 ( 1 )
2x + y - z = 3 ( 2 )
3x - y - 2z = - 4 ( 3 )
( 1 ) + ( 2 ): 3x + 3y = 12 ( 4 )
( 2 ) × 2: 4x + 2y - 2z = 6 ( 2 )'
( 3 ) - ( 2 )': - x - 3y = - 10 ( 5 )
( 4 ) - ( 5 ): 4x = 22
x = 22/4 ( simplificando: 11/2 )
substiruindo x = 11/2 em ( 5 )
- 11/2 - 3y = - 10
- 3y = - 10 + 11/2 ( tirando o MMC )
-6y/2 = - 20/2 + 11/2
- 6y = - 9/2
y = 3/4
substituindo x = 11/2 e y = 3/4 em ( 1 )
11/2 + 3/2 + z = 9 ( tirando o MMC )
11/2 + 3/2 + 2z/2 = 18/2
2z/2 = 18/2 - 14/2
2z/2 = 4/2
z = 2