The equation you provided is:

\[
9x + 6y = 42
\]

We can simplify or solve for one variable in terms of the other. Let's simplify the equation first by dividing through by the greatest common factor of 9, 6, and 42, which is 3.

Dividing the equation by 3:

\[
\frac{9x}{3} + \frac{6y}{3} = \frac{42}{3}
\]

This simplifies to:

\[
3x + 2y = 14
\]

Now you have the simplified form of the equation. If you want to solve for either \( x \) or \( y \), let me know, and I can help you with that as well.

Would you like to proceed with solving for one of the variables?

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Here are some related questions:
1. How do we solve for \( x \) or \( y \) in the simplified equation \( 3x + 2y = 14 \)?
2. What does the graph of the equation \( 3x + 2y = 14 \) look like?
3. Can you express \( y \) in terms of \( x \) or vice versa?
4. How does changing the constant on the right-hand side affect the solution?
5. Can this equation be used in a system of equations to find an exact solution?

**Tip**: Always check if you can simplify an equation by dividing all terms by a common factor to make solving easier.

Learn how to simplify and solve the linear equation 9x + 6y = 42. This tutorial guides you through dividing by the greatest common factor to simplify the equation into 3x + 2y = 14. Suitable for students in Grades 6-8.

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