SOLUTION: 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?

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?
==========================================
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.
=================================================================
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.
==================================================================
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?

RELATED QUESTIONS
deos the shaded region of the graph of the system of inequalities y>3 x+y<5 include... (answered by Mathtut)

Does the shaded region of the graph of the system of equations x < 3, x + 7 < 4 include... (answered by Nate)

3. a. Write a system of inequalities whose solution is represented by the shaded region... (answered by ikleyn)

Graph the system of inequalities. y > -3. x >... (answered by College Student)

In graphing a system with two or more inequalities, how do you show the solution on the... (answered by mananth)

Graph the solution set to the system of inequalities and identify each vertex of the... (answered by scianci)

How do you graph the solution set of the following system of linear inequalities in a... (answered by Edwin McCravy)

Given the following inequalities which point is located in the shaded area y<2x-3 (the (answered by stanbon)