Question

Solve the following pairs 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

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

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

Putting `1/(3x+y) = p ` in the given equations, we get

`p + q = 3/4 ... (i)`

`p/2 - q/2 = (-1)/8`

`p - q = (-1)/4 ... (ii)`

Adding (i) and (ii), we get

`2p = 3/4 - 1/4`

2p = 1/2

p = 1/4

Putting the value in equation (ii), we get

1/4 - q = -1/4

`q = 1/4 + 1/4 = 1/2`

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

3x + y = 4 ... (iii)

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

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

Adding equations (iii) and (iv), we get

6x = 6

x = 1 ... (v)

Putting the value in equation (iii), we get

3(1) + y = 4

y = 1

Hence, x = 1 and y = 1