SOLUTION: Solve this simultaneous equation: {{{(3/x) - (4/y) = (1/3)}}}, {{{(2/x) - (5/y) =(1)}}}

     =     (1)

     = 1.    (2)


Introduce new variables  u = ,  v = .  with these variables, the equations take the form


    3u - 4v =       (3)

    2u - 5v = 1.      (4)


To solve it use the Elimination method.


    6u -  8v =     (5)

    6u - 15v = 3      (6)

  ------------------------------- Subtract eq(5) from eq(6)

        -7v = 2  = 

          v = .


Substitute v = -1/3  into equation (6) to get  

    6u = 3 - 5 = -2,

     u         =  = .


ANSWER.  x =  =  = -3.   y =  =  = -3.