The last freaky thing that can happen is that all three planes intersect in a line...
|So, there are a ton of points along that line that work in all three equations. An infinite number!|
When you are doing the elimination method, you'll be working through... adding those equations together... and BOOM!
You'll get this:
Yeah, it's a true statement... But not very helpful.
When this happens, you'll know that the planes all intersect in a line -- and that line IS the answer! In some harder classes, you'll be shown how to find the equation of that line. For now, write something like this:
"The three planes intersect in a line.
So, there are an infinite number of solutions."