Question

Solve the following systems of equations:

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

`15/(x + y) + 7/(x - y) = 10`

Answer 1

Let `1/(x + y) = u` and `1/(x - y) = v`Then, the given system off equations becomes

5u - 2v = -1 .....(i)

15u + 7v = 10 .....(ii)

Multiplying equation (i) by 7, and equation (ii) by 2, we get

35u - 14v = -7 ....(iii)

30u + 14v = 20 ....(iv)

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

`=> 35u + 360u = -7 + 20`

=> 65u = 13

`=> u = 13/65 = 1/5`

Putting `u = 1/5` in equation (i) we get

`5 xx1/5 - 2v = -1`

=> 1 - 2v = -1

`=> -2v = -1-1`

=> -2v = -2

`=> v = (-2)/(-2) = 1`

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

`=> 1/(x + y)  = 1/5`

=> x + y = 5 ....(v)

and `v = 1/(x - y) =1`

=> x - y = 1 ....(vi)

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

2x = 5 + 1

=> 2x = 6

`=> x = 6/2 = 3`

Putting x = 3 in equation (v), we get

3 + y = 5

`=> y = 5 - 3 = 2`

Hence, solution of the given system of equation is x = 3, y = 2.