Put the above system in augmented matrix form and do a row reduction step. First simplifiy row one, and then subtracting c times row one into row two gives:
2 4 f ~ 1 2 f/2 ~ 1 2 f/2
c d g c d g 0 d-2c g-fc/2
Looking at row 2 we see that d-2c = g-fc/2. And since the matrix is usppose to be consistent, g-fc/2 cannot equal 0. As a result, d-2c cannot equal 0. And so we conclude that d cannot equal 2c