# Simoultaneous equations

• May 11th 2010, 02:36 AM
darksupernova
Simoultaneous equations
Hey there,

Getting very stuck on solving these, ive tried using substitution but i dont know how to rearrange it...
can you help?

$\displaystyle 137.9 = x + \frac{y}{\sqrt{0.05}}$

and

$\displaystyle 275.8 = x + \frac{y}{\sqrt{0.007}}$
• May 11th 2010, 02:46 AM
Bacterius
Hi,
to rearrange for $\displaystyle y$ in the first equation, you can substract $\displaystyle x$ then multiply by $\displaystyle \sqrt{0.05}$. So you find :

$\displaystyle 275.8 = x + \frac{\sqrt{0.05}(137.9 - x)}{\sqrt{0.007}}$

So :

$\displaystyle 275.8 = x + \frac{\sqrt{0.05}}{\sqrt{0.007}} (137.9 - x)$

Setting $\displaystyle a = \frac{\sqrt{0.05}}{\sqrt{0.007}}$ to make it a bit simpler, we are left with :

$\displaystyle 275.8 = x + a (137.9 - x)$

So :

$\displaystyle 275.8 = x + 137.9a - ax$

$\displaystyle 275.8 - 137.9a = x - ax$

$\displaystyle 275.8 - 137.9a = x(1 - a)$

$\displaystyle \frac{275.8 - 137.9a}{1 - a} = x$

Substituting back the value we chose for $\displaystyle a$, we get :

$\displaystyle x = \frac{275.8 - 137.9 \left ( \frac{\sqrt{0.05}}{\sqrt{0.007}} \right )}{1 - \frac{\sqrt{0.05}}{\sqrt{0.007}}} \approx 55.454$

Finding the value of $\displaystyle y$ is now straightforward :)

Does it make sense ? Remember not to get stopped by impressive square roots and stuff : as long as there are no $\displaystyle x$ terms in them, they can be considered a constant (and thus substituted to some letter, $\displaystyle a$ in my example)
• May 11th 2010, 03:46 AM
darksupernova
ah yes that helps thanks very much!
i see the way you got the unkown terms on one side, very nice ;)

Thanks again,

Max
• May 11th 2010, 04:07 AM
Wilmer
Quote:

Originally Posted by darksupernova
Hey there,

Getting very stuck on solving these, ive tried using substitution but i dont know how to rearrange it...
can you help?

$\displaystyle 137.9 = x + \frac{y}{\sqrt{0.05}}$

and

$\displaystyle 275.8 = x + \frac{y}{\sqrt{0.007}}$

Since 275.8 is double 137.9, then you can go this simpler way:

x + y/sqrt(.007) = 2x + 2y/sqrt(.05)
• May 11th 2010, 05:11 AM
HallsofIvy
Seeing "x" alone in both equations, the first thing I would think of is subtracting one equation from the other:
$\displaystyle 275.8 = x + \frac{y}{\sqrt{0.007}}$
$\displaystyle 137.9 = x + \frac{y}{\sqrt{0.05}}$

$\displaystyle 137.9= \frac{y}{\sqrt{0.007}}- \frac{y}{\sqrt{0.05}}= y\left(\frac{1}{\sqrt{0.007}}- \frac{1}{\sqrt{0.05}}\right)$

$\displaystyle 137.9= y\left(\frac{\sqrt{0.05}- \sqrt{0.007}}{\sqrt{(0.05)(.007)}}\right)$

$\displaystyle y= \frac{137.9\sqrt{0.00035}}{\sqrt{0.05}- \sqrt{0.007}}$