Find the equations for the line of intersctions of the planes:
x+y+z=1
x+y=2
I worked it out to be r(t)=3i-j-k+t(i-j)
The ans says:
r(t)=2j-k+t(-i+j)
Hmm. There's something wrong with your method if x = t and x = 3 + t. That's impossible, isn't it? I would suggest row reducing your augmented matrix thus:
$\displaystyle \left[\begin{array}{rrr|r}
1 &1 &1 &1\\
1 &1 &0 &2
\end{array}\right]\to\dots$
You should get a one-parameter family of solutions. What do you get?