Math CentralQuandaries & Queries


Question from Hugh:

xy+x=2y. Solve for y

Hi Hugh,

Suppose the expression was $5y + 5 = 2y$ and you were asked to solve for $y.$ If this were true then my first step would be to add $-2y$ to each side to obtain

\[5y + 5 - 2y = 2y - 2y \mbox{ which simplifies to } 5y - 2y + 5 = 0.\]

Next adding $-5$ to each side and simplifying I get

\[(5 - 2)y = -5.\]

Finally multiplying both sides by $\large \frac{1}{5 - 2}$ and again simplifying I get

\[y = \frac{-5}{5 - 2}= \frac{-5}{3}.\]

Try this same approach with the original expression $xy + x = y.$

Write back if you need more assistance,

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