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.