If `xy != 0` and `sqrt((xy)/(3)) = x`, what is y?
(1) `x/y = 1/3`
(2) `x = 3`

Answer

To solve the equation \( \sqrt{\frac{xy}{3}} = x \) and find the value of \( y \), we will analyze the two given statements.

### Step 1: Start with the given equation
We have the equation:
\[ \sqrt{\frac{xy}{3}} = x \]
To eliminate the square root, we square both sides:
\[ \frac{xy}{3} = x^2 \]

### Step 2: Rearranging the equation
Next, we multiply both sides by 3 to eliminate the fraction:
\[ xy = 3x^2 \]

### Step 3: Isolate \( y \)
Now, we can isolate \( y \) by dividing both sides by \( x \) (since \( xy \neq 0 \), \( x \neq 0 \)):
\[ y = \frac{3x^2}{x} = 3x \]

### Step 4: Analyze the statements
Now we will analyze the two statements to find the value of \( y \).

#### Statement (1): \( \frac{x}{y} = \frac{1}{3} \)
From this statement, we can express \( y \) in terms of \( x \):
\[ y = 3x \]
This matches our earlier result \( y = 3x \). However, this does not provide a specific value for \( y \) since it depends on the value of \( x \).

#### Statement (2): \( x = 3 \)
Substituting \( x = 3 \) into the equation \( y = 3x \):
\[ y = 3(3) = 9 \]
This gives us a specific value for \( y \).

### Conclusion
From the analysis, we find that:
- Statement (1) does not provide a specific value for \( y \).
- Statement (2) gives us \( y = 9 \).

Thus, the correct answer is that we can determine \( y \) using statement (2).

### Final Answer:
The value of \( y \) is \( 9 \).

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