Which of the following points lie in the solution set to the following system of inequalities?

y less than or greater to x - 5
y greater than or equal to -x - 4

(-5, 2)

(5, -2)

(-5, -2)

(5, 2)

Question

Which of the following points lie in the solution set to the following system of inequalities?

y less than or greater to x - 5
y greater than or equal to -x - 4 

 (-5, 2) 

 (5, -2) 

 (-5, -2) 

 (5, 2)

e.mccormick · Answer

Ah, it is a system, so you just try points and see if they are valid or not for the system.  Sometimes this is eaiest if you grap the system and look for overlap.

anonymous · Answer

(-5, -2)  @e.mccormick

e.mccormick · Answer

Id "y less than or greater to x - 5" supposed to be "y less than or equal to x - 5" ?

anonymous · Answer

?

e.mccormick · Answer

Well, look at your text in the question.  The first part is a bit impossible.

e.mccormick · Answer

$$y < > x-5  \ y\ge -x-4 $$ is what you wrote.

anonymous · Answer

can you tell me the answer I don't know it

e.mccormick · Answer

I just need you to clarify the question.  The first line you wrote is impossible. I THINK you meant $y\le x-5$.

anonymous · Answer

yeah that's what I meant

e.mccormick · Answer

K. Then does this help? https://www.desmos.com/calculator/w8enpxgeav

e.mccormick · Answer

The shaded regions show the graphs of each equation.  When you look at an inequality like this in x and y, you want to know where the y values will be.  So you find the line y=x-5, then vecause this is $\le$ you mark out below that (less than that).  Then you graph the line y=-x-4, and because this is really $\ge$ you shade out above that (greater than).  Where you have both, that is a valid solution.

anonymous · Answer

(5, -2)

e.mccormick · Answer

Yes!

e.mccormick · Answer

I hope you can see why so you can get this type of thing on your own.  It is all about the graphs and understanding them.