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.

\begin{align}
a&=\alpha+2\beta\tag{$\color{blue}{1}$}\\
b&=3\alpha+5\beta\tag{$\color{blue}{2}$}\\
3\times(\color{blue}1)-(\color{blue}2):3a-b&=\beta\tag{$\color{blue}{3}$}\\
\text{sub}\ (\color{blue}3)\to(\color{blue}1):a&=\alpha+2(3a-b)\implies\alpha=2b-5a
\end{align}
So we have the solution $\boxed{(\alpha,\beta)=(2b-5a,2a-b)}$.
