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You can solve exactly in algebraic numbers and then get results with any precision by using .n() method:

R.<x,y> = AA[]
eq1 = 2*x^2 + x*y +x - 6
eq2 = 3*x^2 + 2*y^2- y  - 6
sols = R.ideal([eq1,eq2]).variety()
[tuple(map(lambda t: s[t].n(digits=20), R.gens())) for s in sols]

You can solve exactly in algebraic numbers (AA) and then get results in reals with any precision by using .n() method:

R.<x,y> = AA[]
eq1 = 2*x^2 + x*y +x - 6
eq2 = 3*x^2 + 2*y^2- y  - 6
sols = R.ideal([eq1,eq2]).variety()
[tuple(map(lambda t: s[t].n(digits=20), R.gens())) for s in sols]