I’m taking Algebra II this year, and we just finished the chapter on 3 variable equations. This also covered how they can be used to describe planes, and how the solution to them is the intersection of the three planes described in the three equations.

Anyway, I started wondering about how they came up with problems for us to solve - do they just start out with values for x,y and z and just guess and check until they find three equations that work? Or is there a more efficient way of doing it?

One problem in particular seemed especially difficult - it was three planes that intersect in one line, so combining any of the three equations together would always end up with the same equation…and of course, all four equations had to work with the same values for x. What process could they use to do *that?*.