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From the documentation of solve:

algorithm - string (default: ‘maxima’);

Sage uses Maxima by default.

From the documentation of solve:

algorithm - string (default: ‘maxima’);

Sage uses Maxima by default.

Also, more precisely, the source code of solve includes:

if len(s) == 0: # if Maxima's solve gave no solutions, try its to_poly_solve
    try:
        s = m.to_poly_solve(variables)
    except Exception: # if that gives an error, stick with no solutions
        s = []

if len(s) == 0: # if to_poly_solve gave no solutions, try use_grobner
    try:
        s = m.to_poly_solve(variables,'use_grobner=true')
    except Exception: # if that gives an error, stick with no solutions
        s = []

So try Maxima's solve and to_poly_solve, and try the latter with use_grobner=true.