Don't Try to Use Gaussian Elimination

There is a quick way to solve problems like this:

\begin{align*}
m \times a \times t &= \frac{1}{8} \\
m \times a \times h &= 32 \\
m \times t \times h &= \frac{1}{3} \\
a \times t \times h &= 162
\end{align*}

(Source: Brilliant (problem page))

This is a good one. I first attempted to do it by taking the log of both sides of the equations then doing Gaussian elimination with the resulting additive terms, then convert back at the end. After realizing this was neither going to be "quick" nor result in an exact answer likely wanted by the input form, I threw in the towel and looked at the solution. It really is incredibly simple. Just multiply all the equations together:

\[ (math)^3 = 216 \]

And take the cube root:

\[math = 6 \]