Question 457531
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Can someone help me solve the solution of the system using the elemination method?

0.3x - 0.2y = 4
0.5x + 0.5y = 45/23
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        The solution in the post by @mananth is  TOTALLY  and  FATALLY incorrect,

        just because he incorrectly converses 45/23 in the right side of the second equation 

        into decimal fraction  1.96  All his calculations after that are  FAKE.


        Below see my correct solution



<pre>
Your starting equations are

    0.3x - 0.2y = 4	   (1)
    0.5x + 0.5y = 45/23    (2)


To rid fractions, multiply equation (1) by 10; multiply equation (2) by 46.  
You will get

     3x -  2y = 40         (3)
    23x + 23y = 90         (4)


Now I am going to apply the elimination procedure.  
For it, I multiply equation (3) by 23 and multiply equation (4) by 2

    69x - 46y = 920        (5)
    46x + 46y = 180        (6)


Add equations (5) and (6)

    69x + 46x = 920 + 180

        115x  =    1100
   
           x  =    {{{1100/115}}} = {{{220/23}}}.


To find 'y', substitute this found value of 'x' into equation (3)

    {{{3*(220/23)}}} - 2y = 40.

    2y = {{{3*(220/23)}}} - 40 = {{{660/23-40}}} = {{{(660-23*40)/27}}} = {{{-260/23}}}.

     y = {{{-130/23}}}.


<U>ANSWER</U>.  x = {{{220/23}}},  y = {{{-130/23}}}.
</pre>

Solved correctly.