(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I have two equations with three unknowns. Obviously, this is indeterminate and not all three variables can be independently solved. However, I only need (want) to solve for two ratios of the three unknowns. I am writing greatly simplified versions of the equations below:

2. Relevant equations

K1 = Ax + Ay - Bz

K2 = Ax + (A+B)y

I wish to solve for x/y and z/(x+y) in terms of A, B, K1 and K2 only.

3. The attempt at a solution

I have been using excel spreadsheets to attempt numerical solutions and have quickly found the system to STILL be indeterminate even when trying to only solve for these ratios.

When solving for z/(x+y) using eqn. 1, you immediately find it varies with (x+y) as:

z/(x+y) = (A/B) - (K1/(B*(x+y)))

I suspect it is impossible to solve for both (x+y) and (x/y) since knowing both allows you to calculate both x and y. But, on the other hand, I don't want to know (x+y), only z/(x+y).

Any ideas?

Thanks!!

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# 2 equations, 3 unknowns - finding 2 ratios of unknowns

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