Well... I think that picking numbers is the best way to rule out both statements by themselves. I always pick very large/extreme numbers in ineqalities to disprove/rule out the statments. Once you know that you're working with the combined statements, you can match up the inequalities and get:

x-y > -2
x-2y< -6

which becomes:
x - y > -2
-x + 2y > 6

Combined:
y>4

Knowing that we also know that x has to be positive and get the answer.

So we can combine the inequalities from statement 1 and statement 2 without any issues? Since doing so madeit eeasier to figure out that y MUST be a value greater then 4.

Are there any exception as to when you cannot just combine the inequalites from 1 and 2 ?