I have two variables, M and P, whose relationship is described by the following two equations:
 P = 50.5 * M / ( M - 50)  M = C * P
where C is a positive constant. I've arbitrarily designated M to be the output.
In equation 2, M will be positive as long as P is positive. If P is negative, M will be negative. However, if we substitute in P from equation 1 into equation 2 we get:
 M = 50.5 * C + 50 OR M = 0
Now M is guaranteed to be non-negative.
Why is this? I've graphed the equations and noticed that they only intersect in quadrant I. It makes sense that equation 3 would reflect this. But I still feel like there's something mysterious about the whole thing. The phenomenon (M suddenly being only positive) just seems to pop out randomly when looking at it as equations rather than graphically. Is there a fact or concept that will help me demystify the equation side of things?