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.

Learn how to solve the linear equation y = (2y + 1) / 5 with this detailed step-by-step guide. This problem covers fundamental algebraic concepts, focusing on eliminating denominators and isolating variables. Ideal for students in Grades 6-8.

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