Answer:
Part A;
There are many system of inequalities that can be created such that only contain points D and E in the overlapping shaded regions.
Any system of inequalities which is satisfied by (-4, 2) and (-1, 5) but is not satisfied by (1, 3), (3, 1), (3, -3) and (-3, -3) can serve.
An example of such system of equation is
x < 0
y > 0
The system of equation above represent all the points in the second quadrant of the coordinate system.
The area above the x-axis and to the left of the y-axis is shaded.
Part B:
It can be verified that points D and E are solutions to the system of inequalities above by substituting the coordinates of points D and E into the system of equations and see whether they are true.
Substituting D(-4, 2) into the system we have:
-4 < 0
2 > 0
as can be seen the two inequalities above are true, hence point D is a solution to the set of inequalities.
Also, substituting E(-1, 5) into the system we have:
-1 < 0
5 > 0
as can be seen the two inequalities above are true, hence point E is a solution to the set of inequalities.
Part C:
Given that chicken can only be raised in the area defined by y > 3x - 4.
To identify the farms in which chicken can be raised, we substitute the coordinates of the points A to F into the inequality defining chicken's area.
For point A(1, 3): 3 > 3(1) - 4 ⇒ 3 > 3 - 4 ⇒ 3 > -1 which is true
For point B(3, 1): 1 > 3(3) - 4 ⇒ 1 > 9 - 4 ⇒ 1 > 5 which is false
For point C(3, -3): -3 > 3(3) - 4 ⇒ -3 > 9 - 4 ⇒ -3 > 5 which is false
For point D(-4, 2): 2 > 3(-4) - 4; 2 > -12 - 4 ⇒ 2 > -16 which is true
For point E(-1, 5): 5 > 3(-1) - 4 ⇒ 5 > -3 - 4 ⇒ 5 > -7 which is true
For point F(-3, -3): -3 > 3(-3) - 4 ⇒ -3 > -9 - 4 ⇒ -3 > -13 which is true
Therefore, the farms in which chicken can be raised are the farms at point A, D, E and F.
Explanation:
we have that
A (-3,-4)
B (-4,3)
C (2,2)
D (1,-2)
E (5,-4)
F (-3,-13)
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
hope this helps!!.....