Question 282642
{{{system(0.3x-0.2y=4,0.5x+0.5y=45/23)}}}
<pre><font size = 4 color = "indigo"><b>
Remove the decimals in the first equation by multiplying
all the terms by 10

{{{0.3x-0.2y=4}}} becomes:

{{{0.3x*(10)-0.2y*(10)=4*(10)}}} which becomes:

{{{3x-2y=40}}}

Since the second one has a fraction, change the decimals
0.5 to {{{1/2}}}

{{{0.5x+0.5y=45/23)}}} becomes:

{{{(1/2)x+(1/2)y=45/23)}}}

Now multiply through by LCD = 46

{{{(1/2)x*(46)+(1/2)y*(46)=(45/23)*(46)}}}, which becomes:

{{{23x+23y=90)}}}

Now the system is:

{{{system(3x-2y=40,23x+23y=90)}}}

To eliminate the y-terms, multiply the first
equation through by 23 and the second equation through by 2

{{{system(69x-46y=920,46x+46y=180)}}}

Add the two equations together term by term and 
you see the y-terms's cancel out:

{{{system(69x-cross(46y)=920,46x+cross(46y)=180)}}}
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{{{115x=1100}}}

{{{x=1100/115}}}

The fraction will reduce by dividing top and bottom by 5

{{{x=220/23}}}

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Since x is such an ugly looking fraction, do not
substitute it into one of the equations as you
normally do when the solution to the first variable 
is a whole number.  

Instead, go back to this sytem and eliminate the x-terms:

{{{system(3x-2y=40,23x+23y=90)}}}

To eliminate the x-terms do, multiply the first equation 
through by 23 and the second equation through by -3

{{{system(69x-46y=920,-69x-69y=-270)}}}

Add the two equations together term by term and 
you see the x-terms's cancel out:

{{{system(cross(69x)-46y=920,cross(-69x)-69y=-270)}}}

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{{{-115y=650}}}

{{{x=650/(-115)}}}

The fraction will reduce by dividing top and bottom by 5

{{{x=-130/23}}}

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So the solution is an ordered pair of ugly looking fractions:

(x,y) = ({{{220/23}}}, {{{-130/23}}})

Edwin</pre>