So I have a system of PDEs

and I need to figure out if it is elliptic, parabolic, or hyperbolic. So there is this t+s method, where s is the factor associated with the equation and t is associated with the variable, that I am trying to figure out but I don't have a clue. Can someone explain this method? I understand we assign values to the various t and s such that they satisfy some criteria, but I can't seem to figure out this criteria.