eq. 1   2x+ y    =  -4
eq. 2     -2y+4z =   0
eq. 3   3x   -2z = -11

The first equation has no z-term.
So eliminate z from the other two terms.
Multiply eq. 3 by 2 and add term by term:

          -2y+4z =   0
        6x   -4z = -22
        --------------
        6x-2y    = -22

Divide that through by 2

eq. 4   3x- y    = -11

Now we have a system of two equations and two
unknowns:

eq. 1   2x+y =  -4
eq. 4   3x-y = -11

We add them term by term and y will be eliminated:

eq. 1   2x+y =  -4
eq. 4   3x-y = -11
------------------
        5x   = -15
           x = -3

Substitute x = -3 in eq. 4,

eq. 4   3x-y = -11

     3(-3)-y = -11
        -9-y = -11
          -y = -2
           y = 2

Substitute x = -3 in eq. 3 

eq. 3   3x-2z = -11
     3(-3)-2z = -11
        -9-2z = -11
          -2z = -2
            z = 1

Solution (x,y,z) = (-3,2,1)

Edwin