The Gibbs energy of the liquid is usually a convex curve. If the solid phases are pure (the usual assumption), their Gibbs energies are on the ordinates of the Gmx diagram, below the values of the corresponding liquid phase.
For the phase equilibrium, you draw tangent lines from the solid states to the curve. Usually you have two tangents (= two different equilibria, s1l and s2l). At the eutectic point, the tangents coincide.