I have two lines:

$ r\_l:\begin{cases}lx-y=1 \\ x+ly-z=1 \end {cases}\ $

and

$s\_l:\begin{cases}x+y=0 \\ y-lz=-1 \end {cases}\ $

and $l $ is a variable. As $ l $ varies, I have to find their relative position.

I'm guessing that you need to change them to parametric form, equate the equations and do some algebra manipulation, but the last point is where I'm having difficulties.

Can someone help me?

Thanks!