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$$x - 7350 y = 1070$$ $$x - 15080y = 430$$ $$x = ?$$ $$y = ?$$

Hi

I'm trying to find the value of $x$ and $y$ but proving hard any help would be greatly appreciated!

What would be the approach here?

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3  
Substract the second equation form the first to get rid of $x$, then you have $y$ and then in turn $x$. Alternatively use the second equation to express $x$ in terms of $y$ and plug that into the other equation. –  NikolajK Aug 16 '12 at 11:21
    
could you show me with the above example please? –  gilesadamthomas Aug 16 '12 at 11:25

2 Answers 2

Subtracting equation-1 from equation-2, we get

$(x-15080y) - (x-7350y) = 430 - 1070=-640$

$-7730y = -640$

$7730y = 640$

$y = 640/7730=64/773$

Putting the value of $y$ in equation-1, we get

$x - 7350(64/773) = 1070$

$x - 470400/773 = 1070$

$x = 1070 + 470400/773$

$x = 827110+470400/773=1297510/773$

Therefore, $x = 1297510/773, y = 64/773$.

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Substract one of the equations form the other to get rid of $x$, then you have $y$ and then in turn $x$:

$x - 7350\ y = 1070$

$x - 15080\ y = 430$

So

$(x - 7350\ y) - (x - 15080\ y)= 1070-430,$

and this is just an implicit expression for $y$ as $x$ cancels out:

$(-7350 + 15080)\ y= (1070-430)\ \ \Longrightarrow\ \ y= \frac{640}{7730}= \frac{64}{773}.$

Once you got that, the value of $x$ follows by plugging in the obtained $y$ value to one of the equations:

$x - 7350\ y = 1070\ \ \Longrightarrow\ \ x = 1070+7350\ \left(\frac{64}{773}\right)=\frac{1297510}{773}.$


Alternatively use one equation to express $x$ in terms of $y$ and plug that into the other equation:

$x - 15080\ y = 430\ \ \Longrightarrow\ \ x = 430+15080\ y,$

$x - 7350\ y = 1070\ \ \Longrightarrow\ \ (430+15080\ y) - 7350\ y = 1070,$

which is just the same equation as above.


Also, see

http://en.wikipedia.org/wiki/Linear_equation,

http://en.wikipedia.org/wiki/System_of_linear_equations,

http://en.wikipedia.org/wiki/Gauss_elimination,

and here the computational solution:

http://www.wolframalpha.com/input/?i=Solve[{x+-+7350+y+%3D%3D+1070%2C+x+-+15080+y+%3D%3D+430}%2C{x%2Cy}]

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wow thats amazing thanks very much! –  gilesadamthomas Aug 16 '12 at 11:35
    
According to your computation there's a typo in "use the second equation to express". It should be "use the first equation to express". –  Américo Tavares Aug 16 '12 at 11:41
    
@AméricoTavares: I couldn't find it (the second equation is the one with 15080 right?) Anyway, I edited the words "first" and "second" out of the answer as they don't really matter. –  NikolajK Aug 16 '12 at 12:21
    
@gilesadamthomas: I updated it for more detail and also added a second link on "Gauss elimination", which gives the general principle behind the solving algorithm. Also, the "accept answer button" is right below the upvote number on the left. –  NikolajK Aug 16 '12 at 12:23

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