Question

2/x-3/y=15;8/x+5/y=77

Answer 1

HELLO DEAR,

2/x - 3/y = 15
8/x + 5/y = 77


∴ [ let 1/x = p & 1/y = q ]

Now,

2p - 3q = 15------------(1)
8p + 5q = 77-----------(2)



FROM-----(1) & -------(2)
Multiply by (4) in ----(1)

we get,

8p - 12q = 60
8p + 5q = 77
(-)___(-)___(-)
---------------------
-17q = - 17

⇒q = 1 put in --(1)

we get,

2p - 3(1) = 15

⇒2p = 15 + 3

⇒ 2p = 18

⇒p = 9

⇒1/x = 9
∴ [ 1/x = p ]

⇒x = 1/9


AND,

q = 1/y = 1
∴ [ q = 1/y ]

⇒y = 1 , x = 1/9



$VERIFICATION:-$


2/(1/9) - 3(1) = 15

⇒18 - 3 = 15

⇒15 = 15


And,

8/(1/9) + 5(1) = 77


⇒72 + 5 = 77

⇒77 = 77



I HOPE ITS HELP YOU DEAR,
THANKS

Answer 2

HEya..!!!



$Given that: -$
2/x - 3/y = 15
8/x + 5/y = 77


$NOW$
[ 1/x = m , 1/y = n ]

use this in Equation,


2m - 3n = 15--------------(1)
8m + 5n = 77------------(2)



from---(1) AND ------(2)
multiply by (4) in ---(1)

we get,

8m - 12n = 60
8m + 5n = 77
(-)___(-)____(-)
————————
-17n = -17

=> n = 1 put in--(2)



8m + 5(1) = 77

=> 8m = 77 - 5

=> m = 72/8

=> m = 9 , n = 1

we assumed above [ 1/x = m , 1/y = n ]

NOW,

m = 1/x = 9

=> x = 1/9

AND,


n = 1/y = 1

=> y = 1,



I HOPE ITS HELP YOU,