Question 1186043
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Solve this simultaneous equations


{{{(3/x) - (4/y) = (1/3)}}}, {{{(2/x) - (5/y) =(1)}}}
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<pre>
    {{{(3/x) - (4/y)}}} = {{{1/3}}}    (1)

    {{{(2/x) - (5/y)}}} = 1.    (2)


Introduce new variables  u = {{{1/x}}},  v = {{{1/y}}}.  with these variables, the equations take the form


    3u - 4v = {{{1/3}}}      (3)

    2u - 5v = 1.      (4)


To solve it use the Elimination method.


    6u -  8v = {{{2/3}}}    (5)

    6u - 15v = 3      (6)

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

        -7v = 2 {{{1/3}}} = {{{7/3}}}

          v = {{{-1/3}}}.


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

    6u = 3 - 5 = -2,

     u         = {{{-2/6}}} = {{{-1/3}}}.


<U>ANSWER</U>.  x = {{{1/u}}} = {{{1/((-1/3))}}} = -3.   y = {{{1/v}}} = {{{1/((-1/3))}}} = -3.
</pre>

Solved.


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



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