Virtual money exchange theory proposed in [6] is an important theory on finding a set of exchange rates between virtual currencies in rapidly-developed research area of virtual worlds. However, due to mathematical limitation of the employed algorithm, the equation solvability problem emerges in the computation of different virtual exchange rates. This paper provides a solution to identify the solvability problem in the virtual money exchange system and an algorithm to solve this problem by minimally removing unmatched supplies. Evaluation result shows that with this algorithm, the transaction histories can be maximally reserved for the sake of future exchange rate prediction.