Let's work through filling in the math square puzzle step by step.

### Initial Information:
- **Each number from 1 to 9** is used once.
- You have the following equations to satisfy:

#### Row equations:
1. \( X_1 - X_2 + X_3 = 0 \)
2. \( X_4 + X_5 - X_6 = 10 \)
3. \( X_7 - X_8 + X_9 = 6 \)

#### Column equations:
1. \( X_1 + X_4 + X_7 = 23 \)
2. \( X_2 + X_5 + X_8 = 17 \)
3. \( X_3 + X_6 + X_9 = 6 \)

### Approach:
I'll solve for each row and column while ensuring the numbers 1 through 9 are used only once.

#### Step 1: Consider the middle row and column
From the second row, we know:
\[ X_4 + X_5 - X_6 = 10 \]
Try some possibilities for \( X_4, X_5, X_6 \).

Let's begin by trying values:
- \( X_4 = 8 \) 
- \( X_5 = 5 \) 
- \(

Learn how to solve a math square puzzle by applying systems of linear equations. This problem includes equations for rows and columns, covering algebraic concepts suitable for students in Grades 8-10. The step-by-step solution shows how to use the numbers 1 to 9 exactly once.

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