For any system of three equations in three variables, we know that if their planes intersect at a point then there is a unique solution, there are no solutions if any or all three planes are parallel to each other, and that there are infinitely many solutions if they intersect along a common line or all three coincide.
I just can't visualize the difference between the two cases when they intersect along a common line and when they coincide with each other. Isn't the number of solutions infinite in both cases? I have some problem with imagining the third dimension ($z$-axis) in my head, so please tell me in simple words: What is the difference between the infinite number of solutions when the three planes intersect along a common line and when they coincide? Is any of the three variables fixed in a line in any plane?
God, my head spins! What's the difference between the two kinds of infinite solutions here?