x+y-2z=5 .........equation 1
x+z=4.......equation 2
y-z =6........equation 3

Rule for special cases of systems, that applies here:
When one of the equations has no term in one of the letters, eliminate that
letter from the other two.

There are two ways we can go here.  

Equation 3 has no term in x so we would eliminate x from equations 1 and 2.
Then we'd have two equations in only y and z.

OR

Equation 2 has no term in y so we would eliminate y from equations 1 and 3.
Then we'd have two equations in only x and z.

I'll choose the second way:

x + y - 2z = 5 .........equation 1
    y -  z = 6........equation 3

Multiply equation 3 through by -1 so that y will become -y and will cancel
the +y in the first equation:

x + y - 2z =  5 .........equation 1
   -y +  z = -6........equation 3 multiplied through by -1.
-------------------------------------------------------------
x     -  z = -1........equation 4 found by adding term by term.

Now when we put equation 4 together with equation 2 and we have this system:



Adding the two equations just as they are gives




Substituting in




Multiply through by LCD = 2






Substituting in

y - z = 6........equation 3



Multiply through by LCD = 2




Solution:  , , and  

Edwin