a) \(\left\{{}\begin{matrix}2a+b⋮13\\5a-4b⋮13\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}-4a-2b⋮13\\5a-4b⋮13\end{matrix}\right.\)
\(\Rightarrow\left(-4a-2b\right)+\left(5a-4b\right)⋮13\)
\(\Rightarrow a-6b⋮13\)
=>đpcm
b) Ta có: \(\left\{{}\begin{matrix}100a+b⋮7\\7⋮7\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}400a+4b⋮7\\399a⋮7\left(399=7.57\right)\end{matrix}\right.\)
\(\Rightarrow\left(400a+4b\right)-399a⋮7\)
\(\Rightarrow a+4b⋮7\)
=>đpcm
c) Ta có:\(\left\{{}\begin{matrix}3a+4b⋮11\\11⋮11\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}12a+16b⋮11\\11a+11b⋮11\end{matrix}\right.\)
\(\Rightarrow\left(12a+16b\right)-\left(11a+11b\right)⋮11\)
\(\Rightarrow a+5b⋮11\)
=>đpcm
