https://file.aiquickdraw.com/mathbot/file/1727332214875stayc3j5.jpg

This image presents a system of equations and a structure that appears to represent a mathematical puzzle:

1. \( A - B = 5 \)
2. \( C + D = 6 \)
3. The vertical sums (represented by the double lines) seem to indicate additional constraints:
   - \( A + C = 12 \)
   - \( B + D = 9 \)

We can treat this as a system of four equations with four unknowns. Let's solve this step by step.

### System of Equations:
\[
1. \ A - B = 5
\]
\[
2. \ C + D = 6
\]
\[
3. \ A + C = 12
\]
\[
4. \ B + D = 9
\]

I'll solve these equations to find the values of \(A\), \(B\), \(C\), and \(D\).The solution to the system of equations is as follows:

- \( A = 10 \)
- \( B = 5 \)
- \( C = 2 \)
- \( D = 4 \)

These values satisfy all the given conditions in the puzzle.

Would you like further details or have any questions?

Here are some related questions:
1. How do we verify solutions in systems of equations?
2. Can you solve a system with more variables and constraints?
3. What is the importance of substitution in solving equations?
4. How does this method compare to matrix-based solving methods?
5. What happens if we have fewer equations than variables?

**Tip:** When solving systems of equations, always check each solution by substituting the values back into the original equations to ensure accuracy.

Solve the system of equations: A - B = 5, C + D = 6, A + C = 12, B + D = 9

Learn how to solve the system of linear equations involving four variables: A - B = 5, C + D = 6, A + C = 12, and B + D = 9. This problem explores key algebraic concepts and is suitable for students in Grades 8-10.

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