System of Equations/Logic Puzzle Help

**Espionage** · Feb 20th 2013, 04:41 PM

Solve for a+b+c+d+e.

a+b=10
b+c=-7
c+d=3
d+e=11
e+a=1

**Soroban** · Feb 20th 2013, 06:00 PM

Hello, Espionage!

$\text{Solve for }a+b+c+d+e.$

. . $\begin{array}{ccc}a+b&=& 10 \\ b+c&=&\text{-}7 \\ c+d&=&3 \\ d+e&=&11 \\ e+a&=&1\end{array}$

Add the equations:

. . $(a + b)+(b+c)+(c+d)+(d+e)+(e+a) \;=\;10 - 7 + 3 + 11 + 1$

. . $2a + 2b + 2c + 2d + 2e \;=\;18$

. . . . . . $a+b+c+d+e \;=\;9$

**Espionage** · Feb 20th 2013, 06:54 PM

Originally Posted by Soroban

Hello, Espionage!

Add the equations:

. . $(a + b)+(b+c)+(c+d)+(d+e)+(e+a) \;=\;10 - 7 + 3 + 11 + 1$

. . $2a + 2b + 2c + 2d + 2e \;=\;18$

. . . . . . $a+b+c+d+e \;=\;9$

I love you man, thank you.

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