Solution of simple algebraic equations 
Suppose $a=\alpha+2\beta$ and $b=3\alpha+5\beta$. Then by solving this, we get $\alpha=2b-5a$ and $\beta=3a-b$.

I tried substitution method to solve this, but i couldn't get the above solutions viz., $\alpha$ and $\beta$.
I am afraid if this is too basic and it might not be appropriate for this site.

Since $a=\alpha+2\beta$ and $b=3\alpha+5\beta$,$$b-3a=(3\alpha+5\beta)-3(\alpha+2\beta)=-\beta.$$So, $\beta=3a-b$ indeed. And now it is easy to get $\alpha$.
