Question 171295
Does the shaded region of the graph of system of inequalities

{y > 3
{x + y < 5

include the point (5,-2)? How do you know?

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For this to be true, the given point (5, -2) would have to satisfy both inequalities given.

The first inequality is y > 3.

In the point given, y = -2.  See it?  

If you replace y with -2, you will get -2 > 3, which is not true.  So, -2 does not satisfy this first inequality.

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What about the other inequality?

Replace x with 5 and y with - 2.

5 + (-2) < 5

5 - 2 < 5

3 < 5 is true.  The point (5, -2) satisfies the second inequality.

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However, since the given point (5, -2) does NOT satisfy BOTH inequalities, then we can safely say that the shaded region does not include the point 
(5, -2).

Did you follow?