x+y+z=6①
x+2y-3z=4②2x-y+z=5 ③①-②: -y+4z=2,④① *2-③:3y+z=7⑤④*3+⑤:13z=13,得z=1代入④： y=4z-2=2代入①：x=6-y-z=3所以解为x=3,y=2,z=1