Question

if xy/x+y=6/5,xy/y-x=6 (x,y)=?

Answer 1

$<u>Ist equation</u>$

( xy ) / ( x + y ) = 6 / 5

Reciprocal it.

( x + y ) / ( xy ) = 5 / 6

( x / xy ) + ( y / xy ) = 5 / 6

1 / y + 1 / x = 5 / 6 ______ ( 1 )

$<u>2nd equation</u>$

( xy ) / ( x - y ) = 6

Reciprocal it.

( x - y ) / ( xy ) = 1 / 6

( x / xy ) - ( y / xy ) = 1 / 6

1 / y - 1 / x = 1 / 6 ____ ( 2 )

Add ( 1 ) & ( 2 )

1 / y + 1 / y = 5 / 6 + 1 / 6

( 1 + 1 ) / y = ( 5 + 1 ) / 6

2 / y = 6 / 6

$<b>y = 2</b>$

Put this in ( 1 )

1 / 2 + 1 / x = 5 / 6

1 / x = 5 / 6 - 1 / 2

1 / x = ( 5 - 3 ) / 2

1 / x = 2 / 2

1 / x = 1

$<b>x = 1</b>$

Now,

$<i><b><u>( x , y ) = ( 1, 2 )</u></b></i>$