Question: An Error, invalid input, comes from a nonlinear system

I tried to solve a symbolic nonlinear system, which is shown as following:

The S,T,B is three parmeters. And I want to express X and Y by S,T,B.

However, when I use eliminate({},{}), an Error comes as following:

Error, (in SolveTools:-Basis) invalid input: ListTools:-Transpose expects its 1st argument, L, to be of type listlist, but received [[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], FAIL, FAIL, [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]]
 

I have no idea about this problem, who can give a help?

The mw file is given: Eliminate.mw

Thanks!