Systems of equations

Algebra Level 4

$\begin{cases} y^2 + u^2 + v^2 + w^2 = 4x - 1 \\ x^2 + u^2 + v^2 + w^2 = 4y - 1 \\ x^2 + y^2 + v^2 + w^2 = 4u - 1 \\ x^2 + y^2 + u^2 + w^2 = 4v - 1 \\ x^2 + y^2 + u^2 + v^2 = 4w - 1 \\ \end{cases}$

If $y,u,v,w$ and $x$ are real numbers satisfying the systems of equations above, find $y+u+v+w+x$ .