To solve the equation:

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

Step-by-step Solution:

1. Eliminate the denominator: Multiply both sides of the equation by 5 to get rid of the denominator:

$5y = 2y + 1$

2. Isolate the variable: Subtract $2y$ from both sides:

$5y - 2y = 1$

$3y = 1$

3. Solve for $y$: Divide both sides by 3:

$y = \frac{1}{3}$

So, the solution is:

$y = \frac{1}{3}$

Do you want further details or have any questions?

Here are five related questions to expand your understanding:

1. How would the solution change if the equation was $y = \frac{2y - 1}{5}$?
2. Can you solve for $y$ if $y = \frac{3y + 2}{7}$?
3. What if the equation involved a different variable, such as $x = \frac{2x + 1}{5}$?
4. How would you solve $2y = \frac{4y + 2}{5}$?
5. Can you solve $y = \frac{5y + 3}{10}$?

Tip: When dealing with fractions, it's helpful to eliminate the denominator early by multiplying both sides of the equation.