Answer:
The solution for a system of inequalities is the set of all points that satisfy all the inequalities in the system.
For the given system of inequalities, we can graph the inequalities on the x-y plane.
x+y>1
-x+2y>2
-3x-2y<-2
-x-4y<-4
The solution for the system of inequalities is the area of the plane that is common to all of the inequalities, it is the intersection of the feasible regions of the inequalities.
From the graph, we can see that the solution is the area that is inside the line x+y>1 and -x+2y>2 and outside the line -3x-2y<-2 and -x-4y<-4.
The solution is the area between the lines x+y=1 and -x+2y=2 and above the lines -3x-2y=-2 and -x-4y=-4.
Therefore, the solution for the system of inequalities is the set of all points in the x-y plane that is inside the region defined by the lines x+y=1 and -x+2y=2 and above the lines -3x-2y=-2 and -x-4y=-4.