You have the condition

So consider:

So if x = 1 then y could certainly be -10. Thus we can't say .

Let's try the second one:

Here, even if y is positive, x could well be negative. (Try x = -1, y = 10).

So neither condition by itself will guarentee that

What about together? The easiest way to see this is to graph it. (See below.) Where the shaded regions overlap is the solution to the combined inequalities and is a region where both x and y are positive. Thus we have a requirement that , so both conditions are required and sufficient.

-Dan