I am not sure if this belongs in pre-calc or calc and beyond, but I'll put it here. I need help understanding something, ussually I would not do this, I would sit and think until I understand, but it just isn't happening this time and I need help. I am self studying some linear algebra just out of curiousity and just started recently. I am using Gilbert Strang's intro to linear algebra 3rd edition. So basically he is talking about singular cases when a system of linear equations ends up having no solution or infinitely many. Now I understand this would happen if the planes represented by the equations never met (no solution) or met in a line (infinitely many) He gives the following example. u + v + w = 2 2u +3w=5 3u+v +4w=6 He says that this system has no solution, which makes sense since if you add the left hands of the first two equations you get the left hand of the last equation but if you add the first two right hands, they don't add up to the last right hand. My problem is understanding this. He says that if you replaced the 6 in the last equation with a 7, you would get an entire line of solutions (infinitely many). He says the plane "moves to meet the others."... I didn't really understand this so I loaded up maple and tried to understand it by actually plotting the equations. Here is what I got. I don't see a line where they intersect, although I think they most likely do interestect somewhere (but in my oppinion, obviously not everywhere). I entered it into maple as (smartplot3d[u, v, w])(u+v+w = 2, 2*u+3*w = 5, 3*u+v+4*w = 7). What does he mean by "the plane moves to meet the others"? :( ps sorry for the long --- post, couldn't really be shorter though.