Question

Solve the pair of equations by reducing them to a pair of linear equations.
1/(3x + y) + 1/(3x - y) = 3/4
1/2(3x + y) - 1/2(3x - y) = -1/8

Answer 1

Hi ,

Let 1/( 3x + y ) = a ,

1/( 3x - y ) = b

1/( 3x + y ) + 1/( 3x - y ) = 3/4

=> a + b = 3/4

a = 3/4 - b ---( 1 )

1/2( 3x + y ) - 1/2 ( 3x - y ) = -1/8

=>( 1/2 )a - ( 1/2 )b = -1/8

a - b = -1/4 ---( 2 )

substitute ( 1 ) in equation ( 2 ) , we get

3/4 - b - b = -1/4

-2b = -1/4 - 3/4

-2b = -4/4

-2b = -1

b = 1/2

substitute b = 1/2 in equation ( 1 ) , we get

a = 3/4 - 1/2

a = ( 3 - 2 )/4

a = 1/4

Therefore ,

1/( 3x + y ) = a = 1/4=> 3x + y = 4 ---( 3 )

1/( 3x - y ) = b = 1/2=> 3x - y = 2 ---( 4 )

add equations ( 3 ) and ( 4 ) we get

6x = 6

x = 1

substitute x = 1 in equation ( 3 ) , we get

3 + y = 4

y = 4 - 3

y = 1

Therefore ,

x = 1 , y = 1

I hope this helps you.

: )

Answer 2

HELLO DEAR,

GIVEN:-

1/(3x + y) + 1/3(3x - y) = 3/4

1/2(3x + y) - 1/2(3x - y) = -1/8

[put 1/(3x + y) = p , 1/(3x - y) = 3/4]

therefore, p + q = 3/4----------( 1 )

p/2 - q/2 = -1/8

p - q = -1/4----------( 2 )

From------( 1 ) & -----( 2 )

p + q = 3/4

p - q = -1/4

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

2p = 2/4

p = 1/4 [ put in -----( 1 ) ]

p + q = 3/4

1/4 + q = 3/4

q = 3/4 - 1/4

q = (3 - 1)/4

q = 1/2 = 1/(3x - y)

3x - y = 2-------( 3 )

p = 1/(3x + y) = 1/4

3x + y = 4------( 4 )

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

3x + y = 4

3x - y = 2

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

6x = 6

x = 1 [ put in ------( 3 ) ]

3(1) - y = 2

y = 3 - 2

y = 1 , x = 1

I HOPE ITS HELP YOU DEAR,

THANKS