Question 8
Solve the following system of equations for $w$.
$$
\begin{aligned}
& 2w + x + y + z = 1 \\
& w + 2x + y + z = 2 \\
& w + x + 2y + z = 2 \\
& w + x + y + 2z = 1
\end{aligned}
$$
$$
\begin{aligned}
& 2w + x + y + z = 1 \\
& w + 2x + y + z = 2 \\
& w + x + 2y + z = 2 \\
& w + x + y + 2z = 1
\end{aligned}
$$