Question

Solve for x and y:
$$\begin{gathered} \frac{2x+5y}{xy}=6 \\ \frac{4x-5y}{xy}=-3 \end{gathered}$$

Answer 1

The given equations can be written as
$$\begin{gathered} \frac{5}{x}+\frac{2}{y}=6.....\left(i\right) \\ \frac{-5}{x}+\frac{4}{y}=-3.....\left(ii\right) \end{gathered}$$
Adding (i) and (ii), we get
$\frac{6}{y}=3\Rightarrow y=2$
Substituting y = 2 in (i), we have
$\frac{5}{x}+\frac{2}{2}=6\Rightarrow x=1$
Hence, x = 1 and y = 2..