SOLUTION: please help me solve 0.3x-0.2y=4 and 0.5x+0.5y=45/23. The fraction is throwing me off

Algebra ->  Systems-of-equations -> SOLUTION: please help me solve 0.3x-0.2y=4 and 0.5x+0.5y=45/23. The fraction is throwing me off      Log On


   

Question 282642: please help me solve 0.3x-0.2y=4 and 0.5x+0.5y=45/23. The fraction is throwing me off
Answer by Edwin McCravy(20086) About Me  (Show Source):
You can put this solution on YOUR website!
system%280.3x-0.2y=4%2C0.5x%2B0.5y=45%2F23%29

Remove the decimals in the first equation by multiplying
all the terms by 10

0.3x-0.2y=4 becomes:

0.3x%2A%2810%29-0.2y%2A%2810%29=4%2A%2810%29 which becomes:

3x-2y=40

Since the second one has a fraction, change the decimals
0.5 to 1%2F2

0.5x%2B0.5y=45%2F23%29 becomes:

%281%2F2%29x%2B%281%2F2%29y=45%2F23%29

Now multiply through by LCD = 46

%281%2F2%29x%2A%2846%29%2B%281%2F2%29y%2A%2846%29=%2845%2F23%29%2A%2846%29, which becomes:

23x%2B23y=90%29

Now the system is:

system%283x-2y=40%2C23x%2B23y=90%29

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

system%2869x-46y=920%2C46x%2B46y=180%29

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

system%2869x-cross%2846y%29=920%2C46x%2Bcross%2846y%29=180%29
------------
115x=1100

x=1100%2F115

The fraction will reduce by dividing top and bottom by 5

x=220%2F23

----------------
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%283x-2y=40%2C23x%2B23y=90%29

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

system%2869x-46y=920%2C-69x-69y=-270%29

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

system%28cross%2869x%29-46y=920%2Ccross%28-69x%29-69y=-270%29

------------
-115y=650

x=650%2F%28-115%29

The fraction will reduce by dividing top and bottom by 5

x=-130%2F23

--------------

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

(x,y) = (220%2F23, -130%2F23)

Edwin