9. Use the results of problem 8 to find all solutions of each of the following systems
a)
$$\begin{array}{l}
x+y \equiv 1(\bmod 7) \\
x+z \equiv 2(\bmod 7) \\
y+z \equiv 3(\bmod 7)
\end{array}$$
b)
$$\begin{array}{l}
x+2 y+3 z \equiv 1(\bmod 7) \\
x+3 y+5 z \equiv 1(\bmod 7) \\
x+4 y+6 z \equiv 1(\bmod 7)
\end{array}$$
c)
$$\begin{array}{l}
x+y+z \equiv 1(\bmod 7) \\
x+y+w \equiv 1(\bmod 7) \\
x+z+w \equiv 1(\bmod 7) \\
y+z+w \equiv 1(\bmod 7)
\end{array}$$
9. a) $x \equiv 0, y \equiv 1, z \equiv 2(\bmod 7)$
c) $x \equiv 5, y \equiv 5, z \equiv 5, w \equiv 5(\bmod 7)$