x or y? y or z? x or z? x, y, z?

Algebra Level 3

$\large {\begin{cases}x + y + z = 4y + 3 \\ y + z - 7 = 3y \\ z - y - x = y\end{cases}}$

Given that $$x,y$$ and $$z$$ satisfy the system of equations above, find $$2x+3y +z$$.

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