Linear algebra help! Find parametric equations for the line
$$x − 2y + 3z = 4, 2x + y − z = −2$$
I know that the first thing you do is cross the vectors perpendicular to the planes, but I'm having a little trouble finding the point of intersection - can I just set $x, y,$ or $z$ to $0$ and take it from there?

It seems that you are looking for a point lying on the intersection of two planes which is our wanted line. Take $z=t$ into two equations, you get:
$$x-2y+3t=4, 2x+y-t=-2$$
Now eliminate the $y$ by every method you know:
$$5x+t=0$$
Do the same for $x$:
$$y=\frac{7}{5}t-2$$
So the points are as forms:
$$\left(\frac{t}{-5},\frac{7}{5}t-2,t\right)$$
Take for example $t=0$....
