Problem #$3(25$ Points$)$: Show all work to receive full credit.

A causal DT LTI system is described by the difference equation

$y(n)=0\mathrm{.}8y(n-1)+0\mathrm{.}7x(n)-0\mathrm{.}5x(n-1)$

a$)$ Find the impulse response, $h(n),$ of this system using the $z-$transfrom approach. $(15$ Points$)$

b$)$ If an input $,x(z)=\frac{z-1}{z},$ROC: All $z,$ except $z=0,$ is applied to the same system, find Points$)$