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If you have an underdetermined polynomial system of equations, you should probably think of the solution as an algebraic variety.
sage: AA.<x,y> = AffineSpace(QQ, 2)
sage: X = AA.subscheme(x^2+y^2-1)
sage: X
Closed subscheme of Affine Space of dimension 2 over Rational Field defined by:
x^2 + y^2 - 1
sage: X.dimension()
1
Its not clear to me what you mean by "solve"... You should rephrase your question as either a geometric property of the variety or an algebraic property of the defining ideal.
