To solve the equation $7y - 3 = 3 + 6y$, follow these steps:

1. Isolate the variable: Start by getting all terms involving $y$ on one side and constant terms on the other side.

   $7y - 6y = 3 + 3$

   This simplifies to:

   $y = 6$

2. Check the solution: Substitute $y = 6$ back into the original equation to verify.

   $7(6) - 3 = 3 + 6(6)$ $42 - 3 = 3 + 36$ $39 = 39 \quad \text{(True)}$

The solution is $y = 6$.

Would you like more details or have any questions? Here are some related questions you might consider:

1. What methods can be used to solve linear equations?
2. How can you graph the equation $7y - 3 = 3 + 6y$?
3. What are some real-world applications of linear equations?
4. How do you check solutions for equations effectively?
5. Can you explain the concept of slope in relation to linear equations?

Tip: Always check your solution by substituting it back into the original equation!