how to solve system of linear equations of XOR operation? how can i solve this set of equations ? to get values of $x,y,z,w$ ?
$$\begin{aligned} 1=x \oplus y \oplus z \end{aligned}$$
$$\begin{aligned}1=x \oplus y \oplus w \end{aligned}$$
$$\begin{aligned}0=x \oplus w \oplus z \end{aligned}$$
$$\begin{aligned}1=w \oplus y \oplus z \end{aligned}$$
this is not a real example, the variables don't have to make sense, i just want to know the method.

As I wrote in my comment, you can just use any method you know for solving linear systems, I will use Gauss:
$$
\begin{array}{cccc|c||l} \hline
  x & y & z & w &\  & \\ \hline\hline
  1 & 1 & 1 & 0 & 1 & \\
  1 & 1 & 0 & 1 & 1 & \text{$+$ I}\\
  1 & 0 & 1 & 1 & 0 & \text{$+$ I}\\
  0 & 1 & 1 & 1 & 1 & \\ \hline
  1 & 1 & 1 & 0 & 1 & \\
  0 & 0 & 1 & 1 & 0 & \text{III}\\
  0 & 1 & 0 & 1 & 1 & \text{II}\\
  0 & 1 & 1 & 1 & 1 & \text{$+$ III}\\ \hline
  1 & 1 & 1 & 0 & 1 & \\
  0 & 1 & 0 & 1 & 1 & \\
  0 & 0 & 1 & 1 & 0 & \\
  0 & 0 & 1 & 0 & 0 & \text{$+$ III}\\ \hline
  1 & 1 & 1 & 0 & 1 & \\
  0 & 1 & 0 & 1 & 1 & \\
  0 & 0 & 1 & 1 & 0 & \\
  0 & 0 & 0 & 1 & 0 & \\\hline
\end{array}
$$
Now we can conclude $w = 0$ from line 4, which gives $z = 0$ from 3 and $y = 1$ from 2, and finally $x = 0$. So $(x,y,z,w) = (0,1,0,0)$ is the only solution.
