Question

$\frac{2}{x}-\frac{3}{y}=15:\frac{8}{x}+\frac{5}{y}=77$ Find the value of $x$ and $y$.

Answer 1

Consider given equations

$\frac{2}{x}-\frac{3}{y}=15$ ………….(1)

$\frac{8}{x}+\frac{5}{y}=77$ ………….(2)

Let,$u=\frac{1}{x},v=\frac{1}{y}$ then, we get

2u-3v=15 ……………..(3)

8u+5v=77 ………………(4)

From equation (3) $u=\frac{15+3v}{2}$ put in equation (4), we get

$8\times \left(\frac{15+3v}{2}\right)+5v=77$

$4(15+3v)+5v=77$

$60+12v=77$

$v=\frac{17}{12}$

Put the value of v in equation (3).

$2u-3\times \frac{17}{12}=15$

$2u=15+\frac{17}{4}=\frac{77}{4}$

$u=\frac{77}{8}$

Now,

$\frac{1}{x}=u,\frac{1}{y}=v$

$\frac{1}{x}=\frac{77}{8},\frac{1}{y}=\frac{77}{12}$

$x=\frac{8}{77},y=\frac{12}{77}$

Hence, this is the answer,