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If 6xy=x^2y+9y, what is the value of xy?

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Source: — Data Sufficiency |
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by Matt@VeritasPrep » Fri Oct 13, 2017 11:49 am
6xy = x²y + 9y

y * 6x = y * (x² + 9)

If y = 0, this statement will be true, so y = 0 is one solution. To find the other, we divide by y:

6x = x² + 9

0 = x² - 6x + 9

0 = (x - 3)²

and x = 3 is our OTHER solution. With that, we know that either y = 0 or x = 3.

S2 tells us that x ≠ 3, so we MUST have y = 0, and x * y = x * 0 = 0.
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