Translate this problem into a problem involving a system of linear equations. To do this, note that and intersect exactly when there are numbers and that satisfy
rearranging this gives
and
Writing as a system of linear equations gives,
In matrix form,
In other words, and intersect exactly when the above system of linear equations has at least one solution. Using Gaussian Elimination, we obtain
The second row of the last matrix reads
which is impossible. Hence, the system of linear equations has no solution and the lines and do not intersect.