Equivalence of difference equation with system of difference equations I have this system and tried to write down its difference equation as follows

$$    y[n] = b_0v[n] + b_1v[n-1]\\
    v[n] = x[n] - a_1v[n-1]   $$

I was asked to prove that the system can be described by the following difference equation

$$    y[n] + a_1y[n − 1] = b_0x[n] + b_1x[n − 1]$$

Please help me how to prove it.
HINT:

Just express $y[n]$ and $x[n]$ in terms of $v[n-k]$, $k=0,1,\ldots$, and show the equality.