solve breaks on certain repeated inputs

[saliola]

Hi everyone. Thanks for your work on sympy.

I came across an issue when trying to solve a system of equations, and I reduced it to the following example:

>>> solve([z + y/x, - (z + y/x)], [x, y, z])
Traceback (most recent call last):
...
NotImplementedError: no valid subset found

>>> solve([z + y/x, z + y/x], [x, y, z])
Traceback (most recent call last):
...
NotImplementedError: no valid subset found

I would have expected x == -y/z as an answer, and indeed, this is what sympy returns if the second (redundant) equation is removed:

>>> solve([z + y/x], [x, y, z])
[( -y/z, y, z )]

(I verified these tests on https://live.sympy.org/, but I came across them using sympy through sagemath.)

[oscarbenjamin]

I can confirm this with latest sympy master:

In [1]: solve([z + y/x, - (z + y/x)], [x, y, z])
---------------------------------------------------------------------------
NotImplementedError                       Traceback (most recent call last)
<ipython-input-1-07dae630f90a> in <module>
----> 1 solve([z + y/x, - (z + y/x)], [x, y, z])

~/current/sympy/sympy/sympy/solvers/solvers.py in solve(f, *symbols, **flags)
   1095         solution = _solve(f[0], *symbols, **flags)
   1096     else:
-> 1097         solution = _solve_system(f, symbols, **flags)
   1098 
   1099     #

~/current/sympy/sympy/sympy/solvers/solvers.py in _solve_system(exprs, symbols, **flags)
   1866                     solved_syms = list(got_s)
   1867                 else:
-> 1868                     raise NotImplementedError('no valid subset found')
   1869             else:
   1870                 try:

NotImplementedError: no valid subset found

Not sure what that code in _solve_system is doing...