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)
For part A, we want two inequalities that have F and D as solutions, but none of the other points. The easiest way to do this is construct two lines that pass through the origin, and then figure out which way the inequalities need to face based on the points we want to include. Our lines will be: [tex]y=\frac{-3}{2}x[/tex] [tex]y=2x[/tex]
The first line intersects F and the second line intersects D, so we need to figure out which way to point the inequalities so both include the point they do not intersect: [tex]4 \geq \frac{-3}{2}*2[/tex] [tex]3 \geq 2*(-2)[/tex]
So our system is: [tex]y \geq \frac{-3}{2}x[/tex] [tex]y \geq 2x[/tex]
Part B: To verify, plug in the x and y values for D and F and verify that it creates true statements in the system.
Part C: You can plug in the different x, y values for the points. The points which create true statements identify farms where chickens can be raised, while those which create false statements cannot raise chickens.
