Alec, your example did the trick admirably.

Acer, X is indeed symmetric.  (In my problem, it is a normalized covariance matrix.)  At the moment, I am interested only in symbolic solutions for small (n <= 5) variables.  Even in these cases, the number of component equations quickly gets large enough that they are tedious to write out by hand. Eventually, I may look into numerical solutions for larger systems, but for now I am trying to gain insight.  Thanks for the suggestions.