Quote by inknit
For example.
L1: x = 11+3t y = 7+t z = 9+2t
L2: x=6+4t y=2+3t z=7+5t
I was given this problem, and technically these lines don't intersect, right?

The only way both of these lines can be described by the same variable is if the two lines are linearly dependent.
If this is not the case, you need two variables one for each line.