The classification of a family of cubic differential systems in terms of configurations of invariant lines of the type $(3,3)$

In this article we consider the class of non-degenerate real planar cubic vector fields, which possess two real and two complex distinct infinite singularities and invariant straight lines, including the line at infinity, of total multiplicity $7$. In addition, the systems from this class possess configurations of the type $(3,3)$. We prove that there are exactly $16$ distinct configurations of invariant straight lines for this class and present corresponding examples for the realization of each one of the detected configurations.