I've been reading about characteristic equations for recurrence relations and I was wondering how one would solve a simultaneous recurrence, such as
$$f(n) =c_1g(n-1) +c_2f(n-1)+ c_3$$ $$g(n) = d_1f(n-2)+d_2g(n-2)+d_3$$
where $c_i,d_i\in\mathbb{R}$ for $i=1,2,3$