MGMAT Mock 2 DS question!

[RajatS190]

If 2xy + z = 9, what is the value of the positive integer z?

(1) xyz – z^2 = 0

(2) x + y – 3z = -5

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
Both statements TOGETHER are sufficient, but NEITHER one ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.

Hi,
I came across this question in MGMAT Mock and marked (E) as the answer since both the statements are not sufficient to solve and it's wrong. I have seen the Manhattan's explanation for (1) and I didn't understand and I guess it's missing something. The correct answer is (A) (Statement 1 alone is sufficient to answer).

My Version

(1) xyz-z^2=0
> z^2= xyz ------- (i)

We are given 2xy+z=9

Multiplying both sides by z

2xyz+z=9z

From (i) 2z^2+z^2=9z

z^2=9z-2z^2

finally 3z^2-9z=0
3z(z-3) = 0

So, z=0 or z=3

Both the values of Z above are positive and they are integers. Hence, no unique value and we cannot say statement 1 is sufficient. But, the MGMAT explanation you have taken the value of Z=3 and call it as sufficient. Please explain

[RonPurewal]

0 is not positive.