Anwesha Biswas Tithi is a student of Mathematics Discipline Of Khulna University. Now, you have to find her student ID by solving the following system of linear equations:

\[\begin{align*} -3x+2y-6z &=6 \\ 5x+7y-5z &=6 \\ x+4y-2z &=8. \end{align*}\]

If the solution satisfies \(x+y=z,\) what is the value of \(x+y,\) or equivalently \(z?\)

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