Consider the following linear system

$x+z=q$

$y+2w=0$

$x+2z+3w=0$

$2y+3z+pw=3$

in which the numbers $p$ and $q$ are parameters. Under what conditions

does this system have

$($a$)$ a unique solution

$($b$)$ no solution

$($c$)$ infinitely many solutions?