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If I solve for $y$ one way I get one answer, but if I solve a different way (switching the order of the initial equality) I get a completely different answer which apparently is wrong. Just wondering where I am going wrong the second way.

First Way (Correct): $$5y+2 = xy-3x$$ $$5y-xy+2 = -3x$$ $$5y-xy = -3x-2$$ $$y(5-x) = -3x-2$$ $$y = \frac{-3x-2}{5-x}$$

Second Way (Incorrect):

$$xy-3x = 5y+2$$ $$xy-3x-5y = 2$$ $$xy-5y = 2+3x$$ $$y(x-5) = 2+3x$$ $$y = \frac{2+3x}{x-5}$$

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    They are the same. You can multiply the first answer by $1=\frac{-1}{-1}$ to see that it is the same as the second answer. – 2017-01-30

1 Answers 1

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$$y = \frac{-3x-2}{5-x}=\frac{-(3x+2)}{-(x-5)}=\frac{2+3x}{x-5}$$

Both are correct as they are equivalent given $x \neq 5$