Solve[{0==2(-bf-k) pI+2(-bf+b) vI+q+(k^2)r,0==-b vI + (-bf-k) vI + (-bf+b)uI-q,0==-2 b uI+q},{uI,vI,pI}]

Simplify[-((-b bf q-(bf^2) q-b k q-(b^2) (k^2) r-b bf (k^2) r-b (k^3) r)/(2 b (bf+k) (b+bf+k)))]