If $3n+m=14$ and $n+m=1$, find the value of $n-m$.
To solve this problem, I need to find the values of $n$ and $m$ that satisfy both equations. I can use substitution or elimination to do that. I'll solve for $m$ in terms of $n$ using the second equation: $m=1-n$. Then I'll plug that into the first equation and simplify: $3n+(1-n)=14$, $2n+1=14$, $2n=13$, $n=6.5$. Now that I have $n$, I can use it to find $m$: $m=1-n$, $m=1-6.5$, $m=-5.5$. The question asks for the value of $n-m$, so I'll subtract them: $n-m=6.5-(-5.5)=12$. 