Question 692420
<pre>
 3x + 2y +  z = 3
  x - 3y +  z = 4
-6x - 4y - 2z = 1

The idea is to get a system that looks like this:

 Ax + By + Cz = D
      Ey + Fz = G
           Hz = I

And it's OK if the + signs are minuses.

Get rid of the x by multiplying the 2nd eq by -3
and adding the first equation to it:

 3x + 2y +  z =   3
-3x + 9y - 3z = -12
-------------------
     11y - 2z =  -9

So the system is now:

 3x +  2y +  z =  3
      11y - 2z = -9
-6x -  4y - 2z =  1

Get rid of the -6x by multiplying the 1st eq by 2
and adding the third equation to it:

 6x +  4y +  2 =  6
-6x -  4y - 2z =  1
-------------------
            0z =  7

We can stop right here and say there is no solution,
because no value of z multiplied by zero can give 7.
So we write:

No solution, the equations are inconsistent.

Edwin</pre>