This problem doesn't seem to make sense to me.
I have the following three equations:
$ S\alpha+1.06\beta + \mathcal{F} = S\\ T\alpha+1.06\beta + \mathcal{F} = T\\ 98\alpha+\beta + 0\mathcal{F} = 0 $
where $S,T,\alpha,\beta, \mathcal{F}$ are all unknown, but $S \neq T$, and the question asks me to solve for $\mathcal{F}$. Immediately I think, "this must be a mistake, there isn't enough information." However, substituting this into Mathematica yields
$ (\alpha, \beta, \mathcal{F}) = (1,-98,103.88). $
How is this possible?, I would think that the solution space would be very large with so many free variables. Especially since the first two equations seem like duplicates.