<s>[INST] Solve: $4 \log_5 x- \log_5y =1 \quad \&\quad 5\log_5 x+ 3\log_5 y =14$ Find $x,y$ given:
$$4 \log_5 x- \log_5y =1 \quad \&\quad 
5\log_5 x+ 3\log_5 y =14$$
How do I help my son this assignment? Not so good in maths myself 
 [/INST] $$
\begin{align}
4 \log_5 x- \log_5y &=1\tag 1 \\ 
5\log_5 x+ 3\log_5 y &=14\tag 2
\end{align}
$$
Multiplying $(1)$ by $3$ and adding $(1)+(2)$ we have
$$17\log_5 x=17\quad\Longrightarrow\quad \log_5 x=1\quad\Longrightarrow\quad x=5$$
Multiplying $(1)$ by $-5$  and $(2)$ by $4$ and adding $(1)+(2)$ we have
$$17\log_5 y=51\quad\Longrightarrow\quad \log_5 y=51/17=3\quad\Longrightarrow\quad y=5^3=125$$
</s>