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:

3x+2y6z=65x+7y5z=6x+4y2z=8.\begin{aligned} -3x+2y-6z &=6 \\ 5x+7y-5z &=6 \\ x+4y-2z &=8. \end{aligned}

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

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