System of Difference Equations

How would you solve the below?

$bx_t + y_t = a + c$
$y_t = y_{t-1} + \theta (x_{t-1} - y_{t-1})$

My teaching of difference equations has never involved a system so I think I must be missing an easy spot that reduces it to something simple?

You can separate out the difference equations into one which is entirely in x_t, and one which is entirely in y_t; how would you do such a thing if they were just ordinary simultaneous equations? Does that method adapt to difference equations?

Got it.