Originally Posted by

**eumyang** I'm not speaking for HallsofIvy here, but too me you took a lot of steps. I personally wouldn't have gotten rid of the fractions for the first step because the fractions are simple enough. I would have multiplied the first equation by -3, and then add the two equations to get rid of the x:

$\displaystyle \begin{aligned}

\frac{x}{3} + \frac{y}{4} &= 5 \\

x + \frac{3y}{8} &= 12

\end{aligned}$

$\displaystyle \begin{aligned}

-x - \frac{3y}{4} &= -15 \\

x + \frac{3y}{8} &= 12 \\

\end{aligned}$

--------------------

$\displaystyle \begin{aligned}

-\frac{3y}{8} &= -3 \\

-\frac{3y}{8}\left( -\frac{8}{3} \right) &= -3\left( -\frac{8}{3} \right) \\

y &= 8

\end{aligned}$

Or, if you really want to get rid of all of the fractions first, multiply the first equation by **12** and the second equation by **-8**. After combining you'll get rid of the y.