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*}
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
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*}
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
7
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*}
train