11. Find all integer solutions of the following systems of linear diophantine equations
a)
$$\begin{array}{l}
x+y+z=100 \\
x+8 y+50 z=156
\end{array}$$
b)
$$\begin{array}{l}
x+y+z=100 \\
x+6 y+21 z=121
\end{array}$$
c)
$$\begin{array}{l}
x+y+z+w=100 \\
x+2 y+3 z+4 w=300 \\
x+4 y+9 z+16 w=1000
\end{array}$$
11. a) $x=98-6 n, y=1+7 n, z=1-n$
b) no solution
c) $x=50-n, y=-100+3 n, z=150-3 n, w=n$