# Thread: Simoultaneous equations

1. ## 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?

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

and

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

2. Hi,
to rearrange for $y$ in the first equation, you can substract $x$ then multiply by $\sqrt{0.05}$. So you find :

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

So :

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

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

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

So :

$275.8 = x + 137.9a - ax$

$275.8 - 137.9a = x - ax$

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

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

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

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

Finding the value of $y$ is now straightforward

Does it make sense ? Remember not to get stopped by impressive square roots and stuff : as long as there are no $x$ terms in them, they can be considered a constant (and thus substituted to some letter, $a$ in my example)

3. ah yes that helps thanks very much!
i see the way you got the unkown terms on one side, very nice

Thanks again,

Max

4. 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?

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

and

$275.8 = x + \frac{y}{\sqrt{0.007}}$
Since 275.8 is double 137.9, then you can go this simpler way:

x + y/sqrt(.007) = 2x + 2y/sqrt(.05)

5. Seeing "x" alone in both equations, the first thing I would think of is subtracting one equation from the other:
$275.8 = x + \frac{y}{\sqrt{0.007}}$
$137.9 = x + \frac{y}{\sqrt{0.05}}$

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

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

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