Managing inconsistencies in databases is an old, but recurring, problem. An inconsistent database is a database that violates one or more integrity constraints. In the real-world, inconsistent databases arise in several different contexts, including data warehousing and information integration. The framework of database repairs and consistent query answering (CQA) is a principled way of handling inconsistencies. In this work, we propose a novel approach that has a potential to build a comprehensive and scalable CQA system. We report preliminary experimental results on a prototype CQA system CAvSAT (Consistent Answering via Satisfiability), implemented using this approach.