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.