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To solve this problem, we need to subtract the equation \( 3y - x = 8 \) from the equation \( 3y + x = 13 \).

### Step-by-step solution:

1. The first equation is: 
   \[
   3y + x = 13
   \]
2. The second equation is:
   \[
   3y - x = 8
   \]
   
3. Now, subtract the second equation from the first equation:

   \[
   (3y + x) - (3y - x) = 13 - 8
   \]

4. Simplify both sides:
   \[
   3y + x - 3y + x = 13 - 8
   \]
   \[
   2x = 5
   \]

This gives the equation \( 2x = 5 \).

From this, we can see that:

\[
A = 2 \quad \text{and} \quad B = 5
\]

### Final Answer:
- \( A = 2 \)
- \( B = 5 \)

Would you like more details or have any questions?

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Here are 5 related questions to further explore the topic:

1. How do you solve systems of linear equations using substitution?
2. What is the method for solving systems of equations using elimination?
3. Can we apply the same method if we have more than two equations?
4. How does the result change if we switch the order of subtraction?
5. What are the graphical interpretations of these two equations?

**Tip:** Always check your final result by substituting back into the original equations to verify accuracy.

Find the values of A and B to write the equation that is formed when 3y - x = 8 is subtracted from 3y + x = 13.

Learn how to subtract two linear equations, 3y + x = 13 and 3y - x = 8, to form the equation 2x = 5 and find the values of A and B. This problem demonstrates key algebraic techniques used in solving systems of linear equations. Suitable for students in Grades 9-10.

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