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How can I solve this symbolic nonlinear system?

I meet a interesting nonlinear system in the analysis of an mechanics problem. This system can be shown as following:

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wherein, the X and Y is the solutions. A, B, S, and T is the symbolic parameters.

I want to express X and Y with A, B, S, T. Who can give me a help, thanks a lot!

PS:the mw file is given here.

A_symbolic_nonlinear_system.mw


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