Differential equations signal theory question?

Question

We have the system in the figure.I have to find the differential equation that describes the system.Now,the equation is x(k-1)-y(k-1)=y(k),but I don't understand why.I mean I have studied systems and this looks simple,but for some reason I cant put the pieces together..

Answer 1

At the far left, we see that we are adding the $x$ and $y$ signals, and the $y$ signal has been made negative, so we have $x(k)-y(k)$. Then, as we move towards the centre, the signal is delayed by 1, so we obtain $x(k-1)-y(k-1)$. That signal is then output as the value for $y(k)$.