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 \(y+u+v+w+x\).