Question

Solve the pair of equations by reducing them to a pair of linear equations.
5/(x + y) - 2/(x - y) = -1
15/(x + y) + 7/(x - y) = 10 where x≠0, y≠0

Answer 1

Hi ,

It is given that ,

5/(x + y ) - 2/( x - y ) = -1 ----( 1 )

15/(x + y ) + 7/( x - y ) = 10 ---( 2 )



Let 1/( x + y ) = a ,

1/( x - y ) = b

Now ,

5a - 2b = -1 ---( 3 )

15a+ 7b = 10 ---( 4 )

Do 3 × ( 1 ) - ( 2 ), we get

15a - 6b = - 3

15a + 7b = 10
_____________

- 13b = - 13

b = ( -13 )/( -13 )

b = 1

Substitute b = 1 in equation ( 3 ) ,

we get

5a - 2( 1 ) = -1

5a = -1 + 2

5a = 1

a = 1/5

Therefore ,

1/( x + y ) = a = 1/5

=> x + y = 5 ---( 5 )

1/( x - y ) = b = 1

=> x - y = 1 -----( 6 )

add ( 5 ) and ( 6 ) , we get

2x = 6

x = 6/2

x = 3 ,

substitute x = 3 in equation ( 5 ) , we get

3 + y = 5

y = 2

Therefore ,

x = 3 , y = 2

I hope this helps you.

: )

Answer 2

HELLO DEAR,

GIVEN:-

5/(x + y) - 2/(x - y) = -1

15/(x + y) + 7/(x - y) = 10

put [1/(x + y) = p , 1/(x - y) = q]

therefore,

5p - 2q = -1-----------( 1 )

15p + 7q = 10----------( 2 )

from-----------( 1 ) &----------( 2 )

multiply------( 1 ) by "3"

15p - 6q = -3

15p + 7q = 10

--------------------

-13q = -13

q = 1 [ put in ---------( 1 ) ]

we get,

5p - 2(1) = -1

5p = -1 + 2

p = 1/5 = 1/(x + y)

x + y = 5---------( 3 )

AND, q = 1 = 1/(x - y)

x - y = 1----------( 4 )

from-------( 3 ) &-------( 4 )

x + y = 5

x - y = 1

-------------

2x = 6

x = 3 [ put in -----( 3 ) ]

3 + y = 5

y = 2

I HOPE ITS HELP YOU DEAR,

THANKS