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

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Question 1186043: Solve this simultaneous equation:
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Answer by ikleyn(52779)   (Show Source): You can put this solution on YOUR website!
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Solve this simultaneous equations

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     =     (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.

Solved.

Introducing new variables is one of standard methods solving such equations.


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To see many other similar solved problems,  look into the lesson
    - Solving systems of non-linear equations by reducing to linear ones
in this site.



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