Question

Solve the following systems of equations:

`3/x - 1/y = -9`

`2/x + 3/y  = 5`

Answer 1

Let 1/x = u and 1/y Then, the given system of equations becomes

3u - v = -9  ....(i)

2u + 3v = = 5   ....(ii)

Multiplying equation (i) by 3 an equation (ii) by 1, we get

9u - 3v = -27 ....(iii)

2u + 34v = 5  ...(iv)

Adding equation (i) and equation (ii), we get

9u + 2u - 3v + 3v = -27 + 5

=> 11u = -22

`=> u = (-22)/11 = -2`

Putting u = -2 in equation (iv), we get

`2 xx (-2) + 3v = 5` 

`=> -4 + 3v = 5`

=> 3v = 5  + 4

=> v = 9/3 = 3

Hence `x = 1/u = 1/(-2) = (-1)/2` and `y = 1/v = 1/3`

So, the solution of the given system of equation is `x = (-1)/2 , y = 1/3`