ÖMO 1988 Problem 4

Let $a_{ij}$ be nonnegative integers such that $a_{ij}=0$ if and only if $i>j$ and that $\sum_{j=1}^{1988}a_{ij}=1988$ holds for all $i=1,...,1988$ . Find all real solutions of the system of equations:

$\sum_{j=1}^{1988} (1+a_{ij})x_j=i+1, 1 \le i \le 1988$ .