  We consider real polynomial systems $f=g=0$ in two variables where $f$ has
$t\geq 3$ monomial terms and $g$ has $3$ monomials terms. We prove that the
number of positive isolated solutions of such a system does not exceed $3\cdot
2^{t-2} - 1$. This improves the bound $2^t - 2$ obtained in [T.-Y. Li, J.-M.
Rojas and X. Wang, 2003]. This also refines for $t=4,\ldots,9$ the bound
$2t^3/3 + 5t$ obtained in [P. Koiran, N. Portier and S. Tavenas, 2015]. Our
proof is based on a delicate analysis of the Groethendieck's dessin d'enfant
associated to some rational function determined by the system. For $t=3$, it
was shown in [T.-Y. Li, J.-M. Rojas and X. Wang, 2003] that the sharp bound is
five, and if this bound is reached, then the Minkowski sum of the associated
Newton triangles is an hexagon. A further analysis of Groethendieck's dessin
d'enfant allows us to show that if the bound five is reached, then there exist
two consecutive edges of the hexagon which are translate of two consecutive
edges of one Newton triangle.
