find x and y value in simple equation

Question

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

Hi

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

What would be the approach here?

Answer 1

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:

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

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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.

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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}]