Solve for a+b+c+d+e.
a+b=10
b+c=-7
c+d=3
d+e=11
e+a=1
Hello, Espionage!
$\displaystyle \text{Solve for }a+b+c+d+e.$
. . $\displaystyle \begin{array}{ccc}a+b&=& 10 \\ b+c&=&\text{-}7 \\ c+d&=&3 \\ d+e&=&11 \\ e+a&=&1\end{array}$
Add the equations:
. . $\displaystyle (a + b)+(b+c)+(c+d)+(d+e)+(e+a) \;=\;10 - 7 + 3 + 11 + 1$
. . $\displaystyle 2a + 2b + 2c + 2d + 2e \;=\;18$
. . . . . . $\displaystyle a+b+c+d+e \;=\;9$