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)