  A central problem of linear algebra is solving linear systems. Regarding
linear systems as equations over general semirings (V,otimes,oplus,0,1) instead
of rings or fields makes traditional approaches impossible. Earlier work shows
that the solution space X(A;w) of the linear system Av = w over the class of
semirings called join-blank algebras is a union of closed intervals (in the
product order) with a common terminal point. In the smaller class of max-blank
algebras, the additional hypothesis that the solution spaces of the 1x1 systems
Av = w are closed intervals implies that X(A;w) is a finite union of closed
intervals. We examine the general case, proving that without this additional
hypothesis, we can still make X(A;w) into a finite union of quasi-intervals.
