To solve for $b$, we will systematically use the given equations and simplify:

1. Given:
   • $a = 13968$
   • $b + c = 7916$
   • $d + e = 6836$
   • $e + f = 10872$
   • $f + g = 15808$
   • $g + h = 16487$
   • $h + i = 22924$
   • $c + i = 19123$
   • $a + h = 21988$
   • $d + g = 6610$

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Step 1: Solve for $h$

From $a + h = 21988$: $h = 21988 - a = 21988 - 13968 = 8020$

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Step 2: Solve for $i$

From $h + i = 22924$: $i = 22924 - h = 22924 - 8020 = 14904$

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Step 3: Solve for $c$

From $c + i = 19123$: $c = 19123 - i = 19123 - 14904 = 4219$

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Step 4: Solve for $b$

From $b + c = 7916$: $b = 7916 - c = 7916 - 4219 = 3697$

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Final Answer:

$b = 3697$

Would you like me to verify or explore related solutions?

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Related Questions:

1. How would you calculate $d$, $e$, $f$, and $g$ in this problem?
2. What is the sum of all the variables in the given equations?
3. Can these equations be represented and solved using matrix algebra?
4. What are the relationships between $a, h,$ and other variables in the system?
5. How would you interpret this problem geometrically or in terms of a graph?

Tip:

When solving systems of equations, organize variables and known values clearly