Question

Are the lines `2x + 3y = 4` and `2x + 3y = 9` parallel, perpendicular or neither?

Answer 1

These lines are parallel. One nice way to see that is to see that any intersection must satisfy `4 = 2x + 3y = 9` which is always false. So the lines do not intersect.

Explanation:

If there is no simultaneous solution of both equations then the lines do not intersect. Since we're dealing with a Euclidean plane that implies that the lines are parallel.

https://en.m.wikipedia.org/wiki/Plane_(geometry)