Question 381352
Consider this: Let z=x+y be some number


So the system 


x+y>4
x+y<-1


is really saying


z > 4
z < -1



So the question is now: what number (z) is BOTH greater than 4 AND less than -1? This is impossible. Since no number exists, this means that there are no solutions to the system of inequalities above.



So there are no solutions to the system 


x+y>4
x+y<-1



Visually, you'll get the following


<img src="http://i150.photobucket.com/albums/s91/jim_thompson5910/Algebra%20dot%20com/system_linear_ineq2.png">


Where the blue shaded region refers to the solution set of x+y>4 and the red shaded region refers to the solution set of x+y<-1. Since the two regions will NEVER intersect (at any point in the xy plane), this means that the solution set is empty.



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Jim