Answer:
a) (x, y) = (1, 7)
Step-by-step explanation:
Let be the following system of inequalties:
[tex]y > x^{2}-4\cdot x -5[/tex]
[tex]y < -x^{2}-5\cdot x +6[/tex]
We can find the right option by evaluating each option in the system of inequalities:
a) (x, y) = (1, 7)
[tex]7 > 1^{2}-4\cdot (1) -5[/tex]
[tex]7 < -1^{2}-5\cdot (1) +6[/tex]
Then,
[tex]7>-8[/tex] (TRUE)
[tex]7<0[/tex] (FALSE)
(1, 7) is not a solution of the system of inequalities.
b) (x, y) = (1, -7)
[tex]-7 > 1^{2}-4\cdot (1) -5[/tex]
[tex]-7 < -1^{2}-5\cdot (1) +6[/tex]
Then,
[tex]-7 > - 8[/tex] (TRUE)
[tex]-7< 0[/tex] (TRUE)
(1, -7) is a solution of the system of inequalities.
c) (x, y) = (1, -5)
[tex]-5 > 1^{2}-4\cdot (1) -5[/tex]
[tex]-5 < -1^{2}-5\cdot (1) +6[/tex]
Then,
[tex]-5 > - 8[/tex] (TRUE)
[tex]-5< 0[/tex] (TRUE)
(1, -5) is a solution of the system of inequalities.
d) (x, y) = (-1, 6)
[tex]6 > (-1)^{2}-4\cdot (-1) -5[/tex]
[tex]6 <(-1)^{2}-5\cdot (-1)+6[/tex]
Then,
[tex]6>0[/tex] (TRUE)
[tex]6 < 12[/tex] (TRUE)
(-1, 6) is a solution of the system of inequalties.
Therefore, we conclude that correct answer is A.
