Probably not the best question title, but didn't come to think of a better description.

Is it possible to let Matlab solve a system of equations for the case where I want to use a specific definition on some of the solutions?

E.g. for a 2-by-2 system Ax = b I can, by hand, derive b1/x1 = a11+(a12*a21)/((Z2)-a22) with Z2=b2/x2 and b2/x2 = a22+(a12*a21)/((Z1)-a11) with Z1=b1/x1 (ignore that I'm going in a circle, I just need to find expressions for bm/xm when specifying the ratio bn/xn for all n different from m)

Ideally I'd like to use Matlab to do this for a 3-by-3 system as the algebra becomes a bit hairy. As I don't have so much experience with the symbolic tool box I thought I'd try with a 2-by-2 system to begin with as it should be easier, but so far I haven't managed to get the correct results.

Any inputs are greatly appreciated.

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