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  2x+y>0 -2x-y>-8
(6,9) 21>0 so TRUE -21<-8 so FALSE
(-2,4) 0=0 so FALSE 0>-8 so TRUE
(0,0) 0=0 so FALSE 0>-8 so TRUE

No solution because none of the ordered pairs give FALSE for both conditions. Each ordered pair satisfies one of the inequalities but not both.

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