  N-dimensional B\"acklund transformation (BT), Cole-Hopf transformation and
Auto-B\"acklund transformation (Auto-BT) of n-dimensional Burgers system are
derived by using simplified homogeneous balance (SHB). By the Auto-BT, another
solution of the n-dimensional Burgers system can be obtained provided that a
particular solution of the Burgers system is given. Since the particular
solution of n-dimensional Burgers system can be given easily by the Cole-Hopf
transformation, then using the Auto-BT repeatedly, more solutions of
n-dimensional Burgers system can be obtained successively
