There are powerful techniques for dealing with matrices that are singular (or very close to singular). These ideas are also applicible to systems with more (fewer) equations than unknowns. The essence of the method relies on the the following
Theorem Let A be an nXn matrix, and let r be its rank. Then
there exists an orthogonal mXm matrix U and an nXn matrix V such
that 
where F is diagonal nXm or the form
The diagonal entries are the singular values of A, and can be arranged
so that 
.
The SVD is used to solve the least-squares problem.
It amounts to finding a ``best'' approximate solution in some sense -
like minimizing the total 
error for all equations, when there are
more equations than unknowns. See NR for specifics.