The given system represents a family of lines passing through the intersection of 2x+y-3=0 and 3x+2y-5=0
These two lines intersect at (1,1).
Now a line throug this system will be the farthest from the point (4,-3) if the line is perpendicular to the line joining (1,1) and (4,-3).
Slope of the line joining (4,-3) and (1,1) is -4/3.
So slope of the required line passing through (1,1) is 3/4.
So the eqn of the line will be 3x-4y+7=0 (there is no option in the question, please check your choice D).
Ashwin (IIT Madras).