Question

Solve :
$\frac{4}{x}+\frac{5}{y}=7;\frac{3}{x}+\frac{4}{y}=5$

Answer 1

$\frac{4}{x}+\frac{5}{y}=7$ $\frac{3}{x}+\frac{4}{y}=5$

Let $u=\frac{1}{x}$ and $v=\frac{1}{y}$

$\therefore 4u+5v=7$ (i)

$3u+4v=5$ (ii)

(i)$\times$ 3 & (ii)$\times 4\times -1$ and perform their addition

$\Rightarrow$ $12u+15v=21$

- $12u-16v=-20$

_________________

$-v=1$

$v=-1$

putting $v=-1$ in (ii)

$3u+4(-1)=5$

$3u=9$

$u=3$

$\therefore$ substituting the values of u and v

$x=\frac{1}{3}$ and $y=-1$