How will I know if the intersection of two planes is a line or a plane if there's an intersection between them??

Question

precal · Answer

if you are given a systems of equations, you will have a solution

precal · Answer

if not, then you would be given a picture to determine

precal · Answer

|dw:1377136963777:dw|kind of hard to draw in 3d

anonymous · Answer

like for example this:
$$x+y+z=1$$$$2x+2y+2z=2$$
I know that they will intersect but how will i know if their intersection is plane or a line:?

anonymous · Answer

Two planes will intersect as a plane only if they are lying right next to each other... i.e. they are the same plane. So if you have one equation that is a multiple of another, like you do here, you know their intersection is a plane: the plane x+y+z=1.

anonymous · Answer

how about if the planes will have a line as their intersection?
can you please give an example??thanks!

anonymous · Answer

Something like:
x+y+z=1,
2x+y+2z=2,
where one equation is not a multiple of the other.

anonymous · Answer

http://www.youtube.com/watch?v=jozabh0lFmo

anonymous · Answer

aahhh.. ok!, thanks a lot:)

anonymous · Answer

And there is of course the final case: e.g. 
x+y+z=1,
x+y+z=2,
where you get an inconsistency and the planes do not intersect at all (as they are parallel).

You're welcome! :)

anonymous · Answer

@cinar i already checked that out, it helped me a little bit, thanks by the way.
@Erin001001 yes ☺