Abstract interpretation was proposed for predicting changes of reaction networks with partial kinetic information in systems biology. This requires to compute the set of difference abstractions of a system of linear equations under nonlinear constraints. We present the first practical algorithm that can compute the difference abstractions of linear equation systems exactly. We also present a new heuristics based on minimal support consequences for overapproximating the set of difference abstractions. Our algorithms rely on elementary modes, first-order definitions, and finite domain constraint programming. We implemented our algorithms and applied them to change prediction in systems biology. It turns out experimentally that the new heuristics is often exact in practice, while outperforming the exact algorithm.