Find the equation of the plane that goes through three points:

A (0, 3, 4)

B (1, 2, 0)

C (-1, 6, 4)

I know there are good algorithms to do this problem with, and I've gotten 6x - 2y + z = -2 as my answer, which is correct to my knowledge.

HOWEVER...the teacher wants to go with a three-variable, three-equation system of equations with the format of z = m(x) + n(y) + c for each point.

That would mean the following equations:

4 = m(0) + n(3) + c

0 = m(1) + n(2) + c

4 = m(-1) + n(6) + c

I'm confused as to why anyone would want us to use a system.

How do I proceed from here to get the same answer as the algorithm got?