Linear system: 3 variables, 2 equations w/o all variables The question asks to find the direction numbers for the line of intersection of the planes: 
$$ x + y + z = 1 , x + z =0 $$ 
I'm comfortable solving these sorts of linear systems when both equations include each variable. However here I'm slightly stuck. 
If I parameterize $y = t$ for instance I have:
$$x = -z$$ 
$$-z + t + z = 1$$
$$t=1$$  
From this I would guess that the directional numbers would be $(-1, 1, 1)$ (or $(1,1,-1)$ depending on if you substitute for $x$ or $z$). However the book lists that it is: $(1,0,-1)$. How did they get $0$ for $y$?

Since $x + z = 0$ we have that $y = 1$(in second equation).  You can see that y does not depend on t.
Therefore, if $x = t$, then $z = -t$ and $y = 1 + 0*t$.
So you have $<1, 0, -1>$
