How do you solve the system #x-y-z=2#, #2x+y+z=8#, and #x+y+z=6#?
This set of equations can not be solved.
Note that adding equations  and  together, we get
But adding equations  and  together, gives us
Since this was asked under "Solving a System of Equations Using a Matrix"
if you need the matrix version of this, here it is (using Gaussian elimination)
The value in the pivot position for