Math CentralQuandaries & Queries


Question from Mark:

What is y as an expression in terms of x?

Hi Mark,

When you commonly see this is where you have an equation involving $x$ and $y$ and perhaps involving other variables and you are asked to write $y$ as an expression in terms of $x.$ This means that you are to manipulate the equation you have to obtain an equivalent equation of the form

\[y = \mbox{ an expression containing x but not y.}\]

For example suppose the original equation is $ x^2 + 3y - 7 - x - y = 0.$ First you only want terms containing $y$ on the left side of the equation so add $-x^2 +7 + x$ to each side to get

\[x^2 + 3y - 7 - x - y -x^2 + 7 + x = -x^2 +7 + x\]

which simplifies to

\[3y - y = x^2 +7 + x \mbox{ or } 2y = x^2 + x + 7.\]

Multiplying each side by $\large \frac12$ yields

\[y = \frac12 \left(x^2 + x + 7\right)\]

which is equivalent to the original equation $ x^2 + 3y - 7 - x - y = 0$ but written as $y$ as an expression in terms of $x.$

I hope this helps,

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