If given that,

\(-y+2x+z=5\)

\(3y-x+2z=0\)

\(2z+6y+5x=3\)

Solve the system of equations. Believe in the new year and you will be able to do it.

**Details**:

- Given further that \(x, y, z\) can be expressed as integers, find the value of \(x+y+z\).

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