Question

if 5/x+3/y=4 and 3/x+5/y=2 then y-x/xy =-------

a) 5 b)6 c)3 d) 1​

Answer 1

Let,

1 / x = X and 1 / y = Y

The equations become :

5X + 3Y = 4

3X + 5Y = 2

First Add both these equations, we get

8X + 8Y = 6

8 ( X + Y ) = 6

X + Y = 6 / 8 = 3 / 4 ______ ( 1 )

Second Subtract these equations, we get

2X - 2Y = 2

2 ( X - Y ) = 2

X - Y = 2 / 2 = 1 _______ ( 2 )

Now,

Add ( 1 ) and ( 2 ) , we get

2X = 1 + ( 3 / 4 )

2X = ( 4 + 3 ) / 4

2X = 7 / 4

X = 7 / 8

Put this value in ( 1 ), we get

( 7 / 8 ) - Y = 1

Y = ( 7 / 8 ) - 1

Y = ( 7 - 8 ) / 8

Y = - 1 / 8

Now,

According to our Assumption,

Y = 1 / y

- 1 / 8 = 1 / y

y = - 8

Also,

X = 1 / x

7 / 8 = 1 / x

x = 8 / 7

Now,

( y - x ) / xy

$= \frac{ - 8 - \frac{8}{7} }{( - 8)( \frac{8}{7} )} \\ \\ = \frac{ \frac{ - 56 - 8}{7} }{ \frac{ - 64}{7} } \\ \\ = \frac{ - 64}{ - 64} \\ \\ = 1$

Hence, the correct option is d).