Question

Solve the following systems of equations:

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

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

Answer 1

Let `1/(3x + 2y) = u and 1/(3x - 2y) = v` Then, the given system of equation becomes

`2u + 3v = 17/5` ....(i)

5u + v = 2 ....(ii)

Multiplying equation (ii) by 3, we get

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

`=> 13u = (30 - 17)/5`

`=> 13u = 13/5`

`=> u = 13/(5 xx 13) = 1/5`

Putting u = 1/5 in eqaution  (ii) we get

`5 xx 1/5 + v = 2`

=> 1 + v = 2

=> v = 2 - 1

=> v = 1

Now `u = 1/(3x + 2y)`

`=> 1/(3x + 2y) = 1/5`

=> 3x + 2y = 5 ....(iv)

And `v = 1/(3x + 2y)`

`=> 1/(3x + 2y ) = 1/5`

=> 3x + 2y = 5 ....(iv)

And `v = 1/(3x + 2y)`

=> 3x - 2y = 1 ...(v)

Adding equation (iv) and (v), we get

6x = 1 + 5

6x = 6

x = 1

Putting 1 x  in equation (v), we get

3 xx 1 + 2y = 5

2y = 5 - 3

2y  = 2

y = 2/2 = 1

Hence, solution of the given system of equation is x = 1, y = 1