Question

2/x+5/y=1 and 60/x-20/y=13
find x and y​

Answer 1

Answer:

$\huge\bold\green{ question }$

$\frac{2}{x} + \frac{5}{y} = 1 \\ \\ \frac{60}{x} - \frac{20}{y} = 13$

let ,

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

$2u + 5v = 1 - - - (1) \\ 60u - 20v = 13 - - (2)$

equation (1)×20 and (2)

$8u + 20v = 4 \\ 60u - 20v = 13$

_____________________

$68u = 17$

$u = \frac{17}{68} \\ u = \frac{1}{4}$

$\huge\light\orange{ value of " X" equation put in equation }$

$2u + 5v = 1 \\ \\ 2 \frac{1}{4} + 5v = 1 \\ \\ \frac{1}{2} + 5v = 1 \\ \\ \frac{1 + 10v}{2} = 1 \\ 1 + 10v = 2 \\ v = \frac{1}{10}$

$we \: assumed \: that \frac{1}{x} = u \: and \: \frac{1}{y} = v$

$\frac{1}{x} = \frac{1}{4} \\ x = 4$

$\frac{1}{y} = \frac{1}{10} \\ = y = 10$