We have

and

Lets simplify these equations. Assuming p = 1/(3x + y) and q = 1/(3x – y),

p + q = 3/4

⇒ 4p + 4q = 3 …(i)

Also,

⇒ p/2 – q/2 = - 1/8

⇒ 4p – 4q = - 1 …(ii)

To solve these equations, we need to make one of the variables (in both the equations) have same coefficient.

The variable p and q in both the equations have same coefficient.

⇒ 8p = 2

⇒ p = 1/4

Substitute p = 1/4 in eq.(i)/eq.(ii), as per convenience of solving.

Thus, substituting in eq.(ii), we get

4(1/4) – 4q = - 1

⇒ 1 – 4q = - 1

⇒ 4q = 2

⇒ q = 1/2

Thus, p = 1/4 and q = 1/2

As p = 1/(3x + y),

⇒

⇒ 3x + y = 4 …(iii)

And q = 1/(3x – y)

⇒

⇒ 3x – y = 2 …(iv)

Adding equations (iii) and (iv) to obtain x and y,

(3x + y) + (3x – y) = 4 + 2

⇒ 6x = 6

⇒ x = 1

Putting the value of x in equation (iv), we get

3(1) – y = 2

⇒ 3 – y = 2

⇒ y = 1

Hence, we have x = 1 and y = 1