We are given the equation:

$2x + 3y = 1$

To find the value of $y$ when $x = 2$, substitute $x = 2$ into the equation:

$2(2) + 3y = 1$

Simplify:

$4 + 3y = 1$

Subtract 4 from both sides:

$3y = 1 - 4$

$3y = -3$

Divide both sides by 3:

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

$y = -1$

Thus, the value of $y$ when $x = 2$ is:

$y = -1$

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Do you want further details or have additional questions? Here are 5 related questions to expand your understanding:

1. What is the slope-intercept form of the equation $2x + 3y = 1$?
2. How do you solve for $x$ if $y = 0$ in the equation $2x + 3y = 1$?
3. What is the graph of $2x + 3y = 1$, and how can you plot it?
4. How do you calculate the intercepts of $2x + 3y = 1$?
5. How would you check the solution for any value of $x$ and $y$?

Tip: Always double-check your calculations, especially when solving equations, to avoid minor errors!