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Find a+b+c, given that \(\begin{align*} ax+by+c&=x+7,\\ a+bx+cy&=2x+6y,\\ ay+b+cx&=4x+y. \end{align*}\)

 Jul 8, 2020
 #1
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Adding gives

 

\((a + b + c)(1 + x + y) = 7(1 + x + y)\)

 

which means a + b + c = 7 if \(x + y \neq -1\).

 

(The formula is easily verifiable by expanding the terms and comparing to what you have after adding the three equations.)

 Jul 8, 2020
edited by MaxWong  Jul 8, 2020
 #2
avatar+798 
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Thanks!

AnimalMaster  Jul 8, 2020

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