-2x-5y-1z=57
     -5y-2z=54
        -5z=35

That is in echelon (or triangular) form.

You start at the bottom and work your way to the top.

Start by solving the bottom equation first:

        -5z=35
          z=-7

Now substitute z=-7 in the middle equation:

     -5y-2z=54
  -5y-2(-7)=54
     -5y+14=54
        -5y=40
          y=-8

Now substitute z=-7 and y=-8 in the top equation:
  
      -2x-5y-z=57
-2x-5(-8)-(-7)=57
      -2x+40+7=57
        -2x+47=57
           -2x=10
             x=-5

(x,y,z) = (-5,-8,-7)

Edwin