The coordinate plane below represents a city. Points A through F are schools in the city.

graph of coordinate plane. Point A is at negative 5, 5. Point B is at negative 4, negative 2. Point C is at 2, 1. Point D is at negative 2, 4. Point E is at 2, 4. Point F is at 3, negative 4.

Part A: Using the graph above, create a system of inequalities that only contains 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)

i dont get it, i need help eith

The coordinate plane below represents a town. Points A through F are farms in the town.

graph of coordinate plane. Point A is at 2, negative 3. Point B is at negative 3, negative 4. Point C is at negative 4, 2. Point D is at 2, 4. Point E is at 3, 1. Point F is at negative 2, 3.

Part A: Using the graph above, create a system of inequalities that only contains points D and F 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 F 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 − 2. Explain how you can identify farms in which chickens can be raised. (2 points)

Part A: To create a system of inequalities that only contains points D and E in the overlapping shaded regions, we need to consider the conditions that restrict the points to the shaded area.

First, we notice that point D has coordinates (-2, 4) and point E has coordinates (2, 4). Therefore, the y-coordinates for both points are the same, which means our inequality will restrict the y-values to be less than or equal to 4.

The equation for this inequality is: y ≤ 4

Next, we observe that point D lies to the right of the y-axis, while point E lies to the left of the y-axis. Hence, our inequality will limit the x-values to be between -2 and 2.

So, we have: -2 ≤ x ≤ 2

Combining these two inequalities, we can write the system of inequalities for points D and E in the overlapping shaded regions as follows:

-2 ≤ x ≤ 2
y ≤ 4

To graph these lines on the coordinate grid above, we draw a solid horizontal line at y = 4. Then, we shade below this line to represent the inequality y ≤ 4. Next, we draw vertical dotted lines at x = -2 and x = 2. Finally, we shade the area between these vertical lines to show the inequality -2 ≤ x ≤ 2. The shaded region where both inequalities overlap represents the area where points D and E lie.

Part B: To verify that points D and E are solutions to the system of inequalities created in Part A, we substitute the coordinates of both points into the inequalities and check if the inequalities hold true.

For point D (-2, 4):
-2 ≤ x ≤ 2 --> -2 ≤ -2 ≤ 2 (this is true)
y ≤ 4 --> 4 ≤ 4 (this is also true)

For point E (2, 4):
-2 ≤ x ≤ 2 --> -2 ≤ 2 ≤ 2 (this is true)
y ≤ 4 --> 4 ≤ 4 (this is also true)

Since all the inequalities hold true when substituting the coordinates of points D and E, we can conclude that both points are solutions to the system of inequalities created in Part A.

Part C: To identify the schools that Timothy is allowed to attend, we need to substitute the coordinates of each school (A, B, C, D, E, F) into the inequality y < 3x - 3 and check if the inequality is true.

Given y < 3x - 3, we can substitute the coordinates of each school into the inequality:

Point A (-5, 5):
5 < 3(-5) -3
5 < -15 - 3
5 < -18 (this is false)

Point B (-4, -2):
-2 < 3(-4) -3
-2 < -12 - 3
-2 < -15 (this is false)

Point C (2, 1):
1 < 3(2) -3
1 < 6 - 3
1 < 3 (this is true)

Point D (-2, 4):
4 < 3(-2) -3
4 < -6 - 3
4 < -9 (this is false)

Point E (2, 4):
4 < 3(2) -3
4 < 6 - 3
4 < 3 (this is false)

Point F (3, -4):
-4 < 3(3) -3
-4 < 9 - 3
-4 < 6 (this is true)

From the substitutions, we can conclude that Timothy is allowed to attend schools C and F, as these are the only two schools that satisfy the condition y < 3x - 3.

Part A:

To create a system of inequalities that only contains points D and E in the overlapping shaded regions, we need to define the inequalities that describe the region they are in.

Looking at the graph, we can see that the shaded regions overlap at the points D and E. The shaded regions are divided by two lines - one horizontal and one vertical.

The horizontal dividing line is the line that passes through points D and E, which have the same y-coordinate of 4. So, the horizontal dividing line will be the equation y = 4.

The vertical dividing line is the line that passes through points D and E, which have the same x-coordinate of -2. So, the vertical dividing line will be the equation x = -2.

Therefore, the system of inequalities that only contains points D and E in the overlapping shaded regions is:
y=4 and x=-2.

To graph these lines, we plot the points D( -2, 4) and E( 2, 4) on the coordinate grid and draw a horizontal line passing through them, which represents the line y=4. Then, we draw a vertical line passing through D and E, which represents the line x=-2.

Finally, we shade the region between these two lines because it is where points D and E are located.

Part B:

To verify that the points D(-2, 4) and E(2, 4) are solutions to the system of inequalities, we substitute these points into the inequalities and check if they satisfy the conditions.

For the horizontal dividing line y = 4, we substitute the y-coordinate of D and E into the equation:
For point D: y = 4 → 4 = 4 (satisfied)
For point E: y = 4 → 4 = 4 (satisfied)

For the vertical dividing line x = -2, we substitute the x-coordinate of D and E into the equation:
For point D: x = -2 → -2 = -2 (satisfied)
For point E: x = -2 → 2 ≠ -2 (not satisfied)

Therefore, D(-2, 4) satisfies both inequalities, but E(2, 4) only satisfies the horizontal dividing line equation.

Part C:

To identify the schools that Timothy is allowed to attend, we need to substitute the x and y coordinates of each school into the inequality y < 3x - 3, which represents Timothy's zone.

For each school's coordinates, substitute x and y into the inequality and check if it satisfies the condition:

For point A(-5, 5): 5 < 3(-5) - 3 → 5 < -15 - 3 → 5 < -18 (not satisfied)
For point B(-4, -2): -2 < 3(-4) - 3 → -2 < -12 - 3 → -2 < -15 (satisfied)
For point C(2, 1): 1 < 3(2) - 3 → 1 < 6 - 3 → 1 < 3 (satisfied)
For point D(-2, 4): 4 < 3(-2) - 3 → 4 < -6 - 3 → 4 < -9 (not satisfied)
For point E(2, 4): 4 < 3(2) - 3 → 4 < 6 - 3 → 4 < 3 (not satisfied)
For point F(3, -4): -4 < 3(3) - 3 → -4 < 9 - 3 → -4 < 6 (satisfied)

Based on the results, Timothy is allowed to attend schools B, C, and F.

jjjjjjjjjjjjjj

mn hn