3x-6y=-48, x-2y=-16 (dividing through by 3), so x=2y-16,
2x+4y-z=21 becomes 2(2y-16)+4y-z=21, 4y-32+4y-z=21, 8y-z=53;
-5x-3y+5z=4 becomes -5(2y-16)-3y+5z=4, -10y+80-3y+5z=4, -13y+5z=-76.
Now we have 2 equations and 2 unknowns: 8y-z=53, which we can write 40y-5z=265 by multiplying by 5, -13y+5z=-76.
Add these last two equations: 27y=189, y=189/27=7.
But 8y-z=53, so z=8y-53=56-53=3.
Also, x=2y-16=14-16=-2.
SOLUTION: x=-2, y=7, z=3.