The coordinate plane below represents a town. Points A through F are farms in the town. graph of coordinate plane. Point A is at negative 3, negative 4. Point B is at negative 4, 3. Point C is at 2, 2. Point D is at 1, negative 2. Point E is at 5, negative 4. Point F is at 3, 4. Part A: Using the graph above, create a system of inequalities that only contains points A and E in the overlapping shaded regions. Explain how the lines will be graphed and shaded on the coordinate grid above. (5 points) Part B: Explain how to verify that the points A and E are solutions to the system of inequalities created in Part A. (3 points) Part C: Chickens can only be raised in the area defined by y < −2x + 4. Explain how you can identify farms in which chickens can be raised. (2 points)

we have that
A (-3,-4)
B (-4,3)
C (2,2)
D (1,-2)
E (5,-4)
using a graph tool
see the attached figure N 1

Part A: Using the graph above, create a system of inequalities that only contains points A and E in the overlapping shaded regions.

A (-3,-4)  E (5,-4)
y<= -3
y>=-5
is a system of a inequalities that will only contain A and E
to graph it, I draw the constant y = -3 and y=-5  and and I shade the region between both lines
see the attached figure N 2

Part B: Explain how to verify that the points A and E are solutions to the system of inequalities created in Part A

we know that
the system of a inequalities is
y<= -3
y>=-5
the solution is all y real numbers belonging to the interval [-5,-3]

therefore
if points A and E are solutions both points must belong to the interval

points A and E have the same coordinate y=-4
and y=-4 is included in the interval 

therefore
both points are solution

Part C: Chickens can only be raised in the area defined by y < −2x + 4. Explain how you can identify farms in which chickens can be raised

step 1
graph the inequality 
y < −2x + 4
see the attached figure N 3
the farms in which chickens can be raised are the points A, B and D
are those that are included in the shaded part