$$y = 2y+\frac{1}{5}$$

$$ \begin{aligned} y &= 2y+\frac{1}{5}&& \text{multiply ALL terms by } \color{blue}{ 5 }. \\[1 em]5y &= 5\cdot2y+5\cdot\frac{1}{5}&& \text{cancel out the denominators} \\[1 em]5y &= 10y+1&& \text{move the $ \color{blue}{ 10y } $ to the left side} \\[1 em]5y-10y &= 1&& \text{simplify left side} \\[1 em]-5y &= 1&& \text{ divide both sides by $ -5 $ } \\[1 em]y &= -\frac{1}{5}&& \\[1 em] \end{aligned} $$

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