Let QSL≥i be the family of quadratic differential systems with invariant lines of total multiplicity at least i and let QSLi denote the family of quadratic systems with invariant lines of total multiplicity exactly i. For any polynomial system the line at infinity is invariant. Thus the family QS of all quadratic systems is the same as QSL≥1. In the papers [1-4] the families of systems QSLi with i = 4, 5, 6 (6 is the maximum number of invariant lines which could have a quadratic system) were completely studied including first integrals and phase portraits. Now we are interested in systems belonging to the family QSL3. We mention that up to now three subfamilies in QSL3 have been investigated. More precisely: (i) the class of LotkaVolterra systems possessing 2 real invariant straight lines intersecting at a finite real point [5]; (ii) the class of quadratic systems possessing 2 complex invariant lines intersecting at a finite real point [6]; (iii) the class of quadratic systems possessing two invariant lines (real or complex) intersecting at an infinite real point [7].We point out that only for the subfamily (iii) there were investigated its limit points within QSL3. To complete the study of the whole family QSL3 we consider here the limit points of the subfamilies (i) and (ii) within QSL3. The main result is the following: A quadratic system in QSL3 possesses one of the 82 possible configurations of invariant lines. Moreover we determine the affine invariant conditions in terms of the invariant polynomials for the realization of each one of these 82 configurations.