If $d-6c=4$ and $2d-9c=20$, find the value of $\frac{d}{c}$.
This problem involves two linear equations in two variables, $d$ and $c$. One way to solve such a system of equations is to use elimination, which means adding or subtracting the equations to eliminate one of the variables. In this case, I notice that if I multiply the first equation by $-2$, I get $-2d+12c=-8$, and then if I add that to the second equation, I get $3c=12$. This means that $c=4$, and I can substitute that into either equation to find $d$. For example, using the first equation, I get $d-6(4)=4$, so $d=28$. Now that I have both $d$ and $c$, I can find the ratio $\frac{d}{c}$. I get $\frac{d}{c}=\frac{28}{4}=7$. 