Answer:
None of the points (1,0), (-1,1), (2,2) and (0,3) makes both inequalities true
Step-by-step explanation:
You are given two inequalities:
[tex]y>-3x+3[/tex]
and
[tex]y>2x-2[/tex]
The attached diagram shows the common set of points which coordinates suit two inequalities.
As you can see all points (1,0), (-1,1), (2,2) and (0,3) do not belong to the common region (only to one of them or even do not belong to both of them)
You can check it analitically:
(1,0):
[tex]0>-3\cdot 1+3=0\ \text{False}\\ \\0>2\cdot 1-2=0\ \text{False}[/tex]
(-1,1):
[tex]1>-3\cdot (-1)+3=6\ \text{False}\\ \\1>2\cdot (-1)-2=-4\ \text{True}[/tex]
(2,2):
[tex]2>-3\cdot 2+3=-3\ \text{True}\\ \\2>2\cdot 2-2=2\ \text{False}[/tex]
(0,3):
[tex]3>-3\cdot 0+3=3\ \text{False}\\ \\3>2\cdot 0-2=-2\ \text{True}[/tex]
