(x , y) = (3 , 5)

Explanation:

$\begin{cases}6x=2y+8&\\ 4x+5y+10=47&\end{cases}$

$\Longleftrightarrow \begin{cases}12x=4y+16&\\ 12x+15y+30=141&\end{cases}$

$\Longleftrightarrow \begin{cases}12x=4y+16&\\ (4y+16)+15y=111&\end{cases}$

$\Longleftrightarrow \begin{cases}12x=4y+16&\\ 19y+16=111&\end{cases}$

$\Longleftrightarrow \begin{cases}12x=4y+16&\\ 19y=95&\end{cases}$

$\Longleftrightarrow \begin{cases}12x=4y+16&\\ y=(95)/(19)=5 &\end{cases}$

$\Longleftrightarrow \begin{cases}12x=20+16=36&\\ y=5 &\end{cases}$

$\Longleftrightarrow \begin{cases}x=3&\\ y=5 &\end{cases}$

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