After using the final element method, in particular we use the Galerkin procedure, we come up with this couple system of equation coupled. You see the Q matrix, which appears in both equations, that means that you cannot solve one equation separately form the other. We see also the forcing terms, one for the solid equation, and the second one for the flow equation.
Finally the K-matrix, which appears here, is a tangent stiffness matrix because we may have non-linear behaviour of the solid phase.