Answer:
Part A) The system of inequalities is
 and
  and   
 
Part B) In the procedure
Part C) The schools that Natalie is allowed to attend are A,B and D
Step-by-step explanation:
Part A: Using the graph above, create a system of inequalities that only contain points C and F in the overlapping shaded regions
we have 
Points C(2,2), F(3,4)
The system of inequalities could be
 -----> inequality A
 -----> inequality A
The solution of the inequality A is the shaded area at the right of the solid line x=2
 -----> inequality B
 -----> inequality B
The solution of the inequality B is the shaded area above of the solid line y=2
see the attached figure N 1 
Part B: Explain how to verify that the points C and F are solutions to the system of inequalities created in Part A 
we know that
If a ordered pair is a solution of the system of inequalities, then the ordered pair must satisfy both inequalities
<em>Verify point C</em>
C(2,2)    
<em>Inequality A</em>
  ----->
 ----->  ----> is true
 ----> is true
<em>Inequality B</em>
 ------>
 ------>  ----> is true
 ----> is true
therefore
Point C is a solution of the system of inequalities
<em>Verify point D</em>
F(3,4)    
<em>Inequality A</em>
  ----->
 ----->  ----> is true
 ----> is true
<em>Inequality B</em>
 ------>
 ------>  ----> is true
 ----> is true
therefore
Point D is a solution of the system of inequalities
Part C: Natalie can only attend a school in her designated zone. Natalie's zone is defined by y < −2x + 2. Explain how you can identify the schools that Natalie is allowed to attend.
we have

The solution of the inequality is the shaded area below the dotted line 
The y-intercept of the dotted line is the point (0,2)
The x-intercept of the dotted line is the point (1,0)
To graph the inequality, plot the intercepts and shade the area below the dotted line
see the attached figure N 2
therefore
The schools that Natalie is allowed to attend are A,B and D