Given the system of equations:

$x+y+z=3$

$y-3z=1$

$2x+y+5z=6$

$($a$)$ Determine the type of system: inconsistent $$ dependent

$($b$)$ If your answer is dependent, find the complete solution. Write $x,y,$ and $z$ as functions of $t,$ where $z=t.$

If your answer is inconsistent, write DNE in the box for all three variables.

$x=$

$y=$

$z=$