We propose a new relational abstract domain for analysing programs with numeric and Boolean variables. The main idea is to represent an abstract state as a set of linear constraints over numeric variables, with every constraint being enabled by a formula over Boolean variables. This allows us, unlike in some existing approaches, to avoid duplicating linear constraints shared by multiple Boolean formulas. To perform domain operations, we adapt algorithms from constraint-only representation of convex polyhedra, most importantly Fourier-Motzkin elimination and projection-based convex hull. We made a prototype implementation of the new domain in our abstract interpreter for Horn clauses. Our initial experiments are, in our opinion, promising and show directions for future improvement.