Why is \(z\) not so special?

Algebra Level 3

\[\begin{cases} x+\lfloor y \rfloor +\{z\}=200 \\ y+\lfloor z \rfloor +\{x\}=190.1 \\ z+\lfloor x \rfloor +\{y\}=178.8 \end{cases} \]

Solve the above system of equations and find \(x+3y\).

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