If 2x + 3y < 15 and 3x - y ≥ -5, which of the following is true?

I first thought there is something wrong with the OA, but it's actually not. But feel free to correct me if I am mistaken.

First, it is important to know the rules of manipulating inequalities.
We can add unequal terms only if the signs point into the same direction and subtract them only if they point into opposite directions.
Adding or subtracting a number or variable from both sides does not affect the sign.
Multiplying or dividing both sides with the same positive number keeps the direction, multiplying or dividing by a negative number flips it.

Knowing that, we can do the following
I \(2x + 3y < 15\)
II \(3x - y \geq 5\)

\(I*3-II*2\)

\(11y < 40\)

\(y < \frac{40}{11}\)

We should now be able to rule out answer C) since we have shown that y can not be equal to 5.

Knowing that y can be 3 which sould be close to the upper limit, we can plug this into the formulae.

I \(2x + 9 < 15\)
\(x < 2\)

Now this first made me think that answer A) should also be true, but y can be also a negative number. So let's do that for y = -11

II \(3x + 11 \geq 5\)
\(x \geq -2\)

Therefore we have shown that x does not always has to be a positive number leaving us with the answer B.
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