Answer:
Part A) The system of inequalities is
[tex]x\geq2[/tex] and [tex]y\geq2[/tex]
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
[tex]x\geq2[/tex] -----> inequality A
The solution of the inequality A is the shaded area at the right of the solid line x=2
[tex]y\geq2[/tex] -----> 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
Verify point C
C(2,2)
Inequality A
[tex]x\geq2[/tex] -----> [tex]2\geq2[/tex] ----> is true
Inequality B
[tex]y\geq2[/tex] ------> [tex]2\geq2[/tex] ----> is true
therefore
Point C is a solution of the system of inequalities
Verify point D
F(3,4)
Inequality A
[tex]x\geq2[/tex] -----> [tex]3\geq2[/tex] ----> is true
Inequality B
[tex]y\geq2[/tex] ------> [tex]4\geq2[/tex] ----> 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
[tex]y < -2x+2[/tex]
The solution of the inequality is the shaded area below the dotted line [tex]y=-2x+2[/tex]
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
