Start the Linear Solver App. Enter a 3*3 set of
equations. Solve if you like. Now touch the 2 variable button on the
screen. The 3rd equation vanishes, the Z's and
their coefficients vanish from the first 2 equations, but the remaining
coeffiicents are unchanged. OK, that's what I would expect.
Now go back to the 3 variable mode. The 3rd equation reappears,
unchanged. But the coefficients of Z in the first 2 equations are set to
0. If you do not notice this you can get some crazy answers.