x-y+z=0,①
4x+2y+z=3,②
25x+5y+z=60 ③
②-①,得3x+3y=3,则x+y=1④
③-①,得24x+6y=60,则4x+y=10⑤
⑤-④,得3x=9,解得x=3
代入④,解得y=-2
代入①,解得z=-5