Recently, a new method (K. Korovin: Conflict Resolution) was published, that makes Fourier-Motzkin elimination efficient for checking systems of linear inequalities. However, the algorithm is based on rational number representation. The topic of the thesis is to investigate the possibilities of a reliable implementation based on floating point computation with conservative rounding. It may also investigate the usability of the algorithm for solving incremental problems, where new inequalities are added online.