i have two equations of two planes that intersect at the origin:

and

as I have three variables,

and two equations, then I will have an infinite number of solutions: either they are both the same plane or they intersect in exactly one line.

I need to prove this!

I am able to show what happens if they are the same plane:

If there is a non-zero

such that

;

;

then the same line, i.e. the points whose co-ordinates satisfy

also satisfy

that is:

Thus they are the same plane.

but I'm completely at a loss to prove they intersect in precisely one line - any help very gratefully apprectiated!