100
the coordinate plane below represents a city. points a through f are schools in the city.
part a: using the graph above, create a system of inequalities that only contain points d 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 d and e are solutions to the system of inequalities created in part a. (3 points)
part c: timothy can only attend a school in his designated zone. timothy's zone is defined by y < 3x − 3. explain how you can identify the schools that timothy is allowed to attend. (2 points)

Part A.

We could take, for example:



For x ≥ -3 we have vertical line (x-intercept = -3) and shaded region on the right side of the line.
For y ≥ 3 we have horizontal line (y-intercept = 3) and shaded region above that line.

Part B.

Simply, substitute x and y coordinates of D and E to the system of inequalities from part A, and check if its is true, what we get.



so point D is a solution,



and point E is also a solution to our system of inequalities.
 
Part C.

There are two ways we could do that. First is the same as in part B. We substitute x and y coordinates of each school and check if inequality is true or false:





So Timothy can attend schools C and F.

We can also draw a graph of that inequality (pic 2).