The New Year Warm-up Equation Solving

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 :

1. Given further that $x, y, z$ can be expressed as integers, find the value of $x+y+z$ .