The given system of lines passes through the point of intersection of the straight lines 2x+y−3=0 and 3x+2y−5=0[L1+lL2=0 form], which is (1,1).The required line will also pass through this point. Further, the line will be farthest from point (4,−3) if it is in direction perpendicular to line joining (1,1) and (4,−3).∴The equation of the required line is