**Background**

I have the following equations:

$$a+b+c=6$$ $$d+e+f=15$$ $$a+d=5$$ $$b+e=7$$ $$c+f=9$$

This is a 2x3 matrix $[a b c, d e f]$ where the marginal totals are fixed. In addition, all of the unknowns are positive.

I incorrectly told a student that he could do this analytically, and he returned with the answer that, no it could not be solved analytically, but provided a solution that uses the method of iterative proportional fitting.

**Question**

Is it possible to find a unique solution (and know it is unique) for the set of six unknowns using iterative proportional fitting or some similar approach?

**Note**

I posted a related question on math.stackexchange that was limited to the analytical solution, where the initial response was that there was no unique solution; a subsequent response led me to the exact trivial solution and now I see why this was closed.