Determine the values of $x, y$, and $z$ for the following set of linear algebraic equations:

(a) $2 x+y-3 z=11$

$4 x-2 y+3 z=8$

$-2 x+2 y-z=-6$

(b) $2 x-y=10$

$-x+2 y-z=0$

$-y+z=-50$