I don't think maxima does polyhedral computations in its assume facility, 
so you probably get the wrong answer.

We do, however, have quite a lot of tools for polyhedral computations:

sage: P = Polyhedron(ieqs=[(1,2), (10,-7)])
sage: P
A 1-dimensional polyhedron in QQ^1 defined as the convex hull of 2 vertices
sage: P.Hrepresentation()
(An inequality (-7) x + 10 >= 0, An inequality (2) x + 1 >= 0)
sage: P.Vrepresentation()
(A vertex at (10/7), A vertex at (-1/2))
sage: P.integral_points()
((0), (1))

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