Question

x+2y=4 3z=-3 x+2y-z=1

Answer 1

X+2y=4 3z=-3 x+2y-z=1  becomes

X+2y=4
3z=-3
x+2y-z=1

If 3z= -3, then z = -1.

Then we have 

X+2y=4         =>                                 x+2y = 4
3z=-3 
x+2y-z=1       => x+2y-(-1)=1        => x+2y = 0

The graphs of these two straight lines never cross, so the system has NO SOLUTION.