3x-y+z=3 (1)
2x+y-3z=11 (2)
x+y+z=12(3)
(1)+(2),得
5x-2z=14
z=(5x-14)/2
(2)-(3),得
x-4z=-1
z=(x+1)/4
(5x-14)/2=(x+1)/4
整理,得
9x=29
x=29/9
z=(x+1)/4=19/18
x=29/9z=19/18代入(3)
y=12-x-z=12-29/9-19/18=139/18
x=29/9y=139/18z=19/18