Which of the following systems has (i) a unique solution?
(ii) infinitely many solutions? (iii) no solution? In each case, find all solutions:
(a)
$$
x-2 y=1,
$$
$$
3 x+2 y=-3 \text {. }
$$
(b)
$$
\begin{aligned}
& 2 x+y+3 z=1 \\
& x+4 y-2 z=-3
\end{aligned}
$$
$$
x+y-2 z=-3,
$$
$$
x-2 y+z=6,
$$
(c)
$$
\begin{aligned}
2 x-y+3 z=7, & \text { (d) } 2 \\
x-2 y+5 z=1 . & x \\
3 x-2 y+z & =4, \\
x+3 y-4 z & =-3, \\
\text { (f) } x-3 y+5 z & =7, \\
2 x-8 y+9 z & =10 .
\end{aligned}
$$
(d)
$$
2 x+y-3 z=-3 \text {, }
$$
$$
\begin{array}{crr}
& x-2 y+5 z=1 . & x-3 y+3 z=10 . \\
x-2 y+2 z-w=3, & 3 x-2 y+z=4, & x+2 y+1
\end{array}
$$
(f)
$$
\begin{aligned}
2 x-3 y+5 z & =7 \\
x-8 y+9 z & =10
\end{aligned}
$$
(g)
$$
\begin{aligned}
x+2 y+17 z-5 w & =50, \\
9 x-16 y+10 z-8 w & =24, \\
2 x-5 y-4 z & =-13, \\
6 x-12 y+z-4 w & =-1 .
\end{aligned}
$$