  We consider the differential equation $Ju'+qu=wf$ on the real interval
$(a,b)$ when $J$ is a constant, invertible skew-Hermitian matrix and $q$ and
$w$ are matrices whose entries are distributions of order zero with $q$
Hermitian and $w$ non-negative. In this situation it may happen that there is
no existence and uniqueness theorem for balanced solutions of a given initial
value problem. We describe the set of solutions the equation does have and
establish that the adjoint of the minimal operator is still the maximal
operator, even though unique continuation of balanced solutions fails.
