.{ 3x-y+z=3 ,2x+y+3=11 ,x+y+z=12
2x+y+3=11 ,得y=11-3-2x,y=8-2x
x+y+z=12 ,得x+8-2x+z=12 ,x=z-4
3x-y+z=3 ,得3x-(8-2x)+z=3,3x-8+2x+z=3,5x+z=11,z=11-5x
5x+z=11,代入x=z-4,得5z-20+z=11,6z=31,z=31/6
x=z-4,代入z=11-5x,得6x=7,x=7/6
3x-y+z=3,代入z=31/6和x=7/6,得21/6-y+31/6=3,
y=(21+31)/6-3,y=26/3-9/3=(26-9)/3,得y=17/3
最后得到：{x=7/6,z=31/6,y=17/3