Looking at the pattern of numbers in the image and the clue that a single algebraic equation applies across all rows, let's analyze the rows to find a consistent mathematical operation:

1. First row: $2, -3, 9, 5$

   • We can test for simple operations (addition, subtraction, etc.) between consecutive numbers. However, there's no obvious linear relationship between these.

2. Second row: $8, ?, 3, 7$

   • The missing number needs to satisfy the same equation that applies to the first row.

3. Third row: $-4, 2, 4, -6$

   • We should look for an operation that fits this sequence.

4. Fourth row: $5, 2, 8, 1$

   • Similarly, analyze the relationship among these numbers.

Let me analyze potential relationships between these numbers more systematically.The differences between consecutive numbers in each row reveal the following patterns:

1. First row $(2, -3, 9, 5)$: The differences between consecutive numbers are $-5, 12, -4$.
2. Third row $(-4, 2, 4, -6)$: The differences are $6, 2, -10$.
3. Fourth row $(5, 2, 8, 1)$: The differences are $-3, 6, -7$.

We are trying to find a consistent pattern that fits all these rows. The second row $(8, ?, 3, 7)$ should follow a similar pattern of differences. Let's denote the missing number as $x$ and check possible values of $x$ by analyzing these difference patterns.

Let me calculate the possible value of $x$.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, based on the analysis so far, the differences between consecutive numbers across the rows seem to follow a certain pattern, and we can infer the missing number by continuing this logic.

Would you like to discuss any other ideas, or should I continue with a manual approach?

Here are five relative questions that may help further exploration:

1. Can the pattern in the third or fourth row give hints about the second row?
2. What happens if you try adding or subtracting numbers in columns instead of rows?
3. Is it possible that the middle number (missing one) is the result of operations on the rest of the row?
4. Could negative numbers play a special role in altering patterns?
5. Are there alternative ways to connect these numbers through multiplication or division?

Tip: When solving number patterns, looking for consistent differences or ratios between consecutive numbers can be very insightful!