# Show consistency of equations

1. Jun 16, 2009

### Gregg

1. The problem statement, all variables and given/known data

Show that the simultanbeous equations

$6x-7y+2z=4$

$6x-y-z=7$

$2x-3y+z=k$

where k is a constant, are consisten only when k=1.

3. The attempt at a solution

Don't know how to start, the determinent of the co-efficient matrix is -9. This means they are independant, which means I cant express multiples of (1) and (2) for (3) right? I tried to get x and y in terms of z, then substitute for (3)... Doesn't work. I need the method.

2. Jun 16, 2009

$$\begin{pmatrix} 2 & -3 & \hphantom{-}1 & k \\ 6 & -7 & \hphantom{-}2 & 4\\ 6 & -1 & -1 & 7 \end{pmatrix}$$