For this case we have the following system of inequations:
[tex]y\leq2x-5\\y> -3x[/tex]
We must replace each of the points and verify that the inequalities are met:
Point A: (1,1)
[tex]1 \leq2 (1) -5\\1 \leq2-5\\1 \leq-3[/tex]
It is not fulfilled!
Point B: (-2,2)
[tex]2 \leq2 (-2) -5\\2 \leq-4-5\\2 \leq-9[/tex]
It is not fulfilled!
Point C: (5,3)
[tex]3 \leq2 (5) -5\\3 \leq10-5\\3 \leq5[/tex]
Is fulfilled!
[tex]3> -3 (5)\\3> -15[/tex]
Is fulfilled!
Point D: (-4,4)
[tex]4 \leq2 (-4) -5\\4 \leq -8-5\\4 \leq -13[/tex]
It is not fulfilled!
Thus, the point that is the solution of inequalities is:
(5,3)
ANswer:
(5,3)
