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?
Answer by midwood_trail(310)   (Show Source):
You can put this solution on YOUR website! 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?
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