Can someone explain to me how to solve this?
Which of the following points lie in the solution set to the following system of inequalities?
y ≤ x - 5
y ≥ -x - 4
A. (-5, 2)
B. (5, -2)
C. (-5, -2)
D. (5, 2)

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- anonymous

- schrodinger

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- agreene

plug and chug would be the easiest way. the points are given in:
(x,y) form, so you can plug them in for the equations, only one set will work on both

- anonymous

I was thinking B

- agreene

For the case of B):
(5,-2)
eqn 1:
2 ≤ 5-5
2 ≤ 0 <--- not true, can't be B.
For the case of C:
(-5,-2)
eqn 1:
-2 ≤ -5 - 5
-2 ≤ -10 <--- not true, can't be C
As it happens, this also rules out A and D.
the actual roots for this system are:
x= 1/2; y =-9/2
and
x>1/2; -x-4≤y≤x-5

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- anonymous

Wait? So, whats the answer? You ruled all of the answers out?

- anonymous

and you made a mistake on the first equation, its suppose to be a negative 2, not positive.

- anonymous

how am I suppose to answer it if all of the answer choices are wrong? this is confusing? lol

- agreene

indeed i did,
-2 ≤ 0 is true,
y ≥ -x - 4
-2 ≥ -5 -4
-2 ≥ -9 is also true,
I'm dumb, sorry...
B is correct.

- anonymous

haha its okay, I do it all the time, hahaha :D Thanks for your help! :)

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