Question

Solve for X and Y

$\frac{40}{x \: + \: y} \: + \: \frac{30}{x \: - \: y} \: = \: 10 \\ \\ \frac{55}{x \: + \: y} \: + \: \frac{40}{x \: - \: y} \: = \: 13$

Answer 1

Answer :

$\binom{ \frac{40}{x + y} + \frac{30}{x - y} = 10 }{ \frac{55}{x + y} + \frac{40}{x - y} = 13 } \\ \\ to \: make \: calculation \: easier \\ substitute \: \: \frac{1}{x + y} = t \: \: and \: \: \frac{1}{x - y} = u \\ \\ \binom{40t + 30u = 10}{55t + 40u = 13} \\ \\ solve \: the \: system \: of \: equations$
$first \: multiply \: multiply \: both \: sides \: of \: 40t + 30u = 10 \\ by \: 4 \\ \\ 160t + 120u = 40 \\ \\ multiply \: both \: sides \: of \: 55t + 40u \: = 13 \\ by \: - 3 \\ \\ - 165t - 120u = - 39 \\ \\ sum \: the \: equations \: vertically \: \\ \\ - 5t = 1 \\ \\ t = - \frac{1}{ 5} \\ \\ put \: the \: value \: of \: t \: in \: 40t \: + 30u = 10 \\ \\ 40 \times ( - \frac{1}{5} ) + 30u = 10 \\ \\ u \: = \: \frac{3}{5}$
$so \: solution \: is \\ \\ t = - \frac{1 }{5} \\ \\ u = \frac{3}{5} \\ \\ verification \: - - \\ \\ \binom{40 \times ( - \frac{1}{5} ) + 30 \times \frac{3}{5} = 10 }{55 \times ( - \frac{1}{5}) + 40 \times \frac{3}{5} = 13 } \\ \\ \binom{10 = 10}{13 = 13} \\ \\ l.h.s \: = \: r.h.s \\ \\ so \: the \: solution \: is \: true$

The value of x any y has been given in the attachment, Have a look there.

In the attachment --

$x = - \frac{5}{3} \\ \\ y = -\frac{10}{3}$