We need to solve the following equation for $y$: $\frac{y-1}{3} = \frac{2y+1}{5}$

1. Problem Description

We need to solve the following equation for $y$:

$\frac{y-1}{3} = \frac{2y+1}{5}$

2. Solution Steps

First, we cross-multiply to eliminate the fractions:

$5(y-1) = 3(2y+1)$

Next, we distribute the numbers on both sides of the equation:

$5y - 5 = 6y + 3$

Now, we want to isolate $y$. Subtract $5y$ from both sides of the equation:

$5y - 5 - 5y = 6y + 3 - 5y$

$-5 = y + 3$

Subtract 3 from both sides of the equation:

$-5 - 3 = y + 3 - 3$

$-8 = y$

Thus, $y = -8$.

3. Final Answer

$y = -8$