problem: If $3m+4n=47$, and $m+n=15$, what is $m$?
solution: Because the question only asks for the value of $m$, we can begin by eliminating $n$. In order to do this, we multiply the second equation by 4, giving us a system of two equations where both coefficients of $n$ are 4: \begin{align*} 3m+4n=47
  \\ 4m+4n=60
  \end{align*}From here, we can just subtract the second equation from the first. This gives us $(3m+4n)-(4m+4n)=47-60$, which simplifies to $-m=-13$ or $m=\boxed{13}$.