If $3p+4q=8$ and $4p+3q=13$, what is $q$ equal to?
I notice that the coefficients of $p$ and $q$ are reversed in the two equations, so I wonder if I can use elimination to get rid of one of them. I try multiplying the first equation by 4 and the second equation by 3, and then subtracting them to eliminate $p$. I get $12p+16q-12p-9q=32-39$, which simplifies to $7q=-7$. Dividing both sides by 7, I get $q=-1$. 