\(a^2+7b=b^2+7a\\ \Rightarrow a^2-b^2+7b-7a=0\\ \Rightarrow\left(a-b\right)\left(a+b\right)-7\left(a-b\right)=0\\ \Rightarrow\left(a-b\right)\left(a+b-7\right)=0\\ \Rightarrow\left[{}\begin{matrix}a=b\\a+b=7\end{matrix}\right.\)
Với \(a=b\Rightarrow a+b=2a=2b\)
Vậy \(\left[{}\begin{matrix}a+b=2a=2b\\a+b=7\end{matrix}\right.\)