The equation given is:

\[
py + 7 = 6y + q
\]

To solve for \(y\), we will rearrange the equation step by step.

1. Subtract \(6y\) from both sides:

\[
py - 6y + 7 = q
\]

2. Factor out \(y\) on the left-hand side:

\[
y(p - 6) + 7 = q
\]

3. Subtract 7 from both sides:

\[
y(p - 6) = q - 7
\]

4. Finally, divide both sides by \((p - 6)\):

\[
y = \frac{q - 7}{p - 6}
\]

So, the solution for \(y\) is:

\[
y = \frac{q - 7}{p - 6}
\]

Let me know if you'd like further details or clarification!

### 5 Related Questions:
1. How would the solution change if \( p = 6 \)?
2. What happens if \( p = q = 0 \)?
3. Can you solve for \( p \) or \( q \) in terms of the other variables?
4. How would you interpret this equation graphically?
5. How does this solution relate to solving systems of equations?

### Tip:
Always check for division by zero when solving equations like this! If \( p = 6 \), the equation becomes undefined.

Learn how to solve the linear equation py + 7 = 6y + q with a detailed step-by-step guide. This problem demonstrates core algebraic techniques like variable isolation and equation rearrangement. Suitable for students in Grades 8-10.

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