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Find $a+b+c$, given that $x+y\neq -1$ and \begin{align*} ax+by+c&=x+7,\\ a+bx+cy&=2x+6y,\\ ay+b+cx&=4x+y. \end{align*}

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  • $\begingroup$ What have you done? $\endgroup$
    – saulspatz
    Commented Jul 26, 2018 at 3:10
  • $\begingroup$ Random hint: $\;1+2+4=6+1=7\,$. But really, you should add some context, and show what you have tried. See How to ask a good question. $\endgroup$
    – dxiv
    Commented Jul 26, 2018 at 3:17

1 Answer 1

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Add the three equations altogether to get:

$(ax+by+c)+(a+bx+cy)+(ay+b+cx)=(ax+bx+cx)+(ay+by+cy)+(a+b+c)= (a+b+c)(x+y+1)=7x+7y+7$

Since $x+y$ is not equal to $-1$, we can divide both sides of the equation by $x+y+1$ to get $a+b+c=(7x+7y+7)/(x+y+1)=7$ which gives us what we wanted.

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