Question

Solve for x and y:

`2/((3x + 2y)) + 3/((3x - 2y)) = 17/5, 5/((3x + 2y)) + 1/((3x - 2y)) = 2`

Answer 1

The given equations are

`2/((3x + 2y)) + 3/((3x - 2y)) = 17/5`   ...(i)

`5/((3x + 2y)) + 1/((3x - 2y)) = 2`   ...(ii)

Substituting `1/(3x + 2y) = u` and `1/(3x - 2y) = v`, in (i) and (ii), we get:

`2u + 3v = 17/5`   ...(iii)

5u + v = 2   ...(iv)

Multiplying (iv) by 3 and subtracting from (iii), we get:

`2u - 15u = 17/5 - 6`

⇒ `-13u = (-13)/5`

⇒ `u = 1/5`

⇒ 3x + 2y = 5   `(∵ 1/(3x + 2y) = u)`   ...(v)

Now, substituting `u = 1/5` in (iv), we get

1 + v = 2

⇒ v = 1

⇒ 3x – 2y = 1   `(∵ 1/(3x - 2y) = v)`   ...(vi)

Adding (v) and (vi), we get:

⇒ 6x = 6

⇒ x = 1

Substituting x = 1 in (v), we get:

3 + 2y = 5

⇒ y = 1

Hence, x = 1 and y = 1.