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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)

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Philip P. | Effective and Affordable Math TutorEffective and Affordable Math Tutor
5.0 5.0 (428 lesson ratings) (428)
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-(x+4) ≤ y ≤ (x-5)   (I assume this is what you meant)
 
I'll do the first one.
  1. Plug in (x=-5,y=2)
 
-(-5+4) ≤ 2 ≤ (-5-5)
 
1 ≤ 2 ≤ -10
 
1 is less than or equal to 2, but 2 is not less than or equal to -10.  So (-5,2) is not a solution.
 
Do the other points the same way.
Michael K. | I can help you pass the class, take the test, or get into the college.I can help you pass the class, take the ...
4.8 4.8 (113 lesson ratings) (113)
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You graph the two inequalities on a coordinate plane.  Each inequality requires shading on one side of the line.  Once you have the shading in place, you graph the four points.  The points which are in the region shaded by both of the inequalities are solutions.