Solving a system of recurrence relations What is the methodology to solve for a system of recurrence relations?
For example:
$X_{n+1} = 4X_n + Y_n$
$Y_{n+1} = 3Y_n + X_n$

A much more simplistic approach, similar to linear equations. You have $$X_{n+1} = 4X_n + Y_n$$ $$Y_{n+1} = 3Y_n + X_n$$ From the second equation, extract $X_n=Y_{n+1}-3Y_n$ which also mean $X_{n+1}=Y_{n+2}-3Y_{n+1}$. Replace now in the first equation to get $$Y_{n+2}-7Y_{n+1}+11Y_n=0$$ which, using the traditional method, leads to $$Y_n=c_1 \left(\frac{1}{2} \left(7-\sqrt{5}\right)\right)^n+c_2 \left(\frac{1}{2}
   \left(7+\sqrt{5}\right)\right)^n$$ Now, reuse $X_n=Y_{n+1}-3Y_n$
