in a Math class we are currently working with Farka's Lemma in order to determine if systems of equations have a solution. In order to do this we need to often find out if systems of multiple inequalities have solutions.
One such example is:
$\ x +z+r≥\theta$
$\ x +y+r≥\theta$
$\ y +z+r≥\theta$
$\ -y -z-r≥\theta$
$\ 2x+2y +2z+1<\theta$
In this case I was told that there is a solution to this system, however I was wondering if there is a general approach I can use to determining if such a system has a solution. In order to use the parkas Lemma I don't need a specific solution, just if there is one or not.
Thank you very much a already in advance,
Marcel