Find $x$ and $y$ value in simple equation $$x - 7350 y = 1070$$
$$x - 15080y = 430$$
$$x = ?$$    $$y = ?$$
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? 
 A: 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}]
A: 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, $x = 1297510/773,  y = 64/773$.
