Question

Solve the following system of equations:

`4/x + 3y = 14`

`3/x - 4y = 23`

Answer 1

`4/x + 3y = 14`

`3/x - 4y = 23`

Let `1/x = p`

The given equations reduce to:

4p + 3y = 14 

`=> 4p + 3y - 14 = 0` ...(1)

3p - 4y = 23

`=> 3p - 4y - 23 = 0` ....(2)

Using cross-multiplication method, we obtain

`p/(-69-56) = y/(-42 - (-92)) = 1/(-16 - 9)`

`p/(-125) = y/50 = (-1)/25`

p = 5, y = -2

`:. p = 1/x = 5`

`x = 1/5`