Question

Is (0,0) a solution of the system y>x and x+y>0?

A: Yes, because (0,0) is the point of intersection of the two boundary lines of this system
B: No, because (0,0) is is a solution to only one of these inequalities
C: Yes, because (0,0) is a solution to both inequalities
D: No, because (0,0) is not a solution to either of these inequalities

Answer 1

Plug the values (x,y)=(0,0) into the inequalities:

$y\ \textgreater \ x \\ 0\ \textgreater \ 0 \\ not \ true \\ \\ x+y\ \textgreater \ 0 \\ 0+0\ \textgreater \ 0 \\ 0\ \textgreater \ 0 \\ not \ true$

0 isn't greater than 0, no (0,0) is not a solution to either of these inequalities.

The answer is D.