What Is The Student ID Of Nur Uddin Vai?

Algebra Level 2

Md Nur Uddin is a student of Mathematics Discipline Of Khulna University. Now, you have to find his student ID by solving the following system of linear equations:

$\begin{aligned} -3x+2y-6z &=6 \\ 5x+7y-5z &=6 \\ x+4y-2z &=8. \end{aligned}$

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