  In this paper, we present a new method for variable elimination in systems of
inequations which is much faster than the Fourier-Motzkin Elimination (FME)
method. In our method, a linear Diophantine problem is introduced which is dual
to our original problem. The new Diophantine system is then solved, and the
final result is calculated by finding the dual inequations system. Our new
method uses the algorithm Normaliz to find the Hilbert basis of the solution
space of the given Diophantine problem. We introduce a problem in the
interference channel with multiple nodes and solve it with our new method.
Next, we generalize our method to all problems involving FME and in the end we
compare our method with the previous method. We show that our method has many
advantages in comparison to the previous method. It does not produce many of
the redundant answers of the FME method. It also solves the whole problem in
one step whereas the previous method uses a step by step approach in
eliminating each auxiliary variable.
