Let's solve the equation step by step to find the x-value when $y = 2$.

The given equation is:

$2x + 3y = 26$

Substitute $y = 2$ into the equation:

$2x + 3(2) = 26$

Now, simplify:

$2x + 6 = 26$

Next, subtract 6 from both sides to isolate the term with $x$:

$2x = 26 - 6$

$2x = 20$

Finally, divide both sides by 2 to solve for $x$:

$x = \frac{20}{2} = 10$

So, when $y = 2$, $x = 10$.

Answer:

$x = 10, \, y = 2$

Would you like further details on this problem? Here are some related questions for you to explore:

1. How would the equation change if $y$ were replaced with a different value?
2. What would happen if we multiplied the entire equation by a constant?
3. How do you solve a system of equations with similar forms?
4. What is the geometric interpretation of the equation $2x + 3y = 26$?
5. How do you graph the line represented by the equation?

Tip: To solve linear equations quickly, always start by substituting known values, then isolate the variable you're solving for!