x+y+z=6 ①
x+2y-3z=4 ②2x-y+z=5 ③①-②: -y+4z=2, ④① *2-③:3y+z=7 ⑤④*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