We are given the equation:

\[
2y - 42 = 8y
\]

To solve for \( y \), follow these steps:

### Step 1: Move all terms involving \( y \) to one side
Subtract \( 2y \) from both sides:

\[
2y - 42 - 2y = 8y - 2y
\]

This simplifies to:

\[
-42 = 6y
\]

### Step 2: Solve for \( y \)
Divide both sides of the equation by 6:

\[
\frac{-42}{6} = y
\]

This simplifies to:

\[
y = -7
\]

Thus, the solution is:

\[
y = -7
\]

Would you like a detailed explanation of any step? 

Here are some related questions:

1. How do we check if a solution is correct in a linear equation?
2. What is the general approach to solving equations with variables on both sides?
3. How would this solution change if the equation was \( 2y - 42 = 8y + 10 \)?
4. How can we solve equations with fractions?
5. What are some common mistakes to avoid when solving linear equations?

**Tip:** Always double-check your solution by plugging it back into the original equation.

Learn how to solve the linear equation 2y - 42 = 8y with a step-by-step solution. This problem involves key algebraic concepts, such as isolating variables and simplifying equations. Suitable for students in Grades 6-8.

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