Solve the following system of equations for $c$:
\begin{align*}
a - b &= 2 (c+d)\\
b &= a-2 \\
d &= c+5
\end{align*}
I notice that the second equation gives me a way to express $b$ in terms of $a$, so I can substitute that into the first equation and get: $a - (a-2) = 2 (c+d)$. This simplifies to $2 = 2 (c+d)$, or $1 = c+d$. Now I have an equation with only $c$ and $d$, but I also notice that the third equation gives me a way to express $d$ in terms of $c$, so I can substitute that into the equation and get: $1 = c + (c+5)$. This simplifies to $1 = 2c + 5$, or $-4 = 2c$, or $c = -2$. This is the value of $c$ that satisfies the system of equations. 