My 800 followers problem!

Algebra Level 5

\[\begin{array} (799(x-y)& +& 800(y-z)& + &801(z-x) & =0 \\ 638401(x-y) & + & 640000(y-z) & +& 641601(z-x) & =800 \end{array}\]

If \(x,y,z\) satisfy the above system of equations then find the value of \(x-2y+z\).