Question

Solve the following simultaneous equation
$\frac{2}{x}-\frac{3}{y}=15;\frac{8}{x}+\frac{5}{y}=77$

Answer 1

$\frac{2}{x}-\frac{3}{y}=15---\left(1\right)$ and $\frac{8}{x}+\frac{5}{y}=77---\left(2\right)$

$\left(4\right)x$ equation $\left(1\right)-$ equation $\left(2\right)$ given

$\frac{8}{x}-\frac{12}{y}=60$

$\frac{\frac{8}{x}+\frac{5}{y}=77--}{\frac{-17}{y}=-17\Rightarrow y=1}$

Putting $y=1$ in equation $\left(1\right)$

$\frac{2}{x}-3=15\Rightarrow \frac{2}{x}=18\Rightarrow x=\frac{1}{x}$

$\therefore x=\frac{1}{9}$ and $y=1$