G1.2 Given that $x=x_{0}$ and $y=y_{0}$ satisfy the system of equations $\left\{\begin{array}{l}\frac{x}{3}+\frac{y}{5}=1 \\ \frac{x}{5}+\frac{y}{3}=1\end{array}\right.$. If $B=\frac{1}{x_{0}}+\frac{1}{y_{0}}$, find the value of $B$.
$$
\frac{x}{3}+\frac{y}{5}=\frac{x}{5}+\frac{y}{3}=1 \Rightarrow \frac{x}{3}-\frac{x}{5}=\frac{y}{3}-\frac{y}{5} \Rightarrow x=y
$$

Sub. $x=y$ into the first equation: $\frac{x}{3}+\frac{x}{5}=1 \Rightarrow x=y=\frac{15}{8} \Rightarrow B=\frac{16}{15}$