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This puzzle appears to involve a grid of numbers with some empty yellow squares that need to be filled. The grid shows equations that combine both addition and subtraction, and the goal is likely to find the values of the yellow squares that satisfy all the conditions.

Let me break down the puzzle:

### The grid contains these equations:

1. First row: \[ \text{Yellow square} + \text{Yellow square} = 8 \]
2. Second row: \[ \text{Yellow square} + \text{Yellow square} = 6 \]
3. Third row: \[ \text{Yellow square} - \text{Yellow square} = 13 \]
4. Fourth row: The numbers 13 and 8 are provided as results for the rows or columns.

The objective is to find the values of the yellow squares such that they satisfy the equations. I will now solve this systematically.

Let:
- The first yellow square in the first row be \( x \),
- The second yellow square in the first row be \( y \),
- The first yellow square in the second row be \( z \),
- The second yellow square in the second row be \( w \).

We have the following system of equations:
1. \( x + y = 8 \)
2. \( z + w = 6 \)
3. \( z - w = 13 \)

Now, I will solve these equations.The solution to the system of equations yields:

1. \( x = 8 - y \), where \( y \) is free to take a value.
2. \( z = \frac{19}{2} = 9.5 \)
3. \( w = -\frac{7}{2} = -3.5 \)

This means:
- The values for \( z \) and \( w \) are \( 9.5 \) and \( -3.5 \) respectively.
- For \( x \) and \( y \), the sum \( x + y = 8 \), but the values of \( x \) and \( y \) can vary as long as this sum holds.

Would you like to explore further or solve with a specific constraint for \( x \) and \( y \)?

Here are some related questions for further thought:
1. Could \( x \) and \( y \) take integer values?
2. How do negative numbers affect the logic of the puzzle?
3. What if \( z \) or \( w \) were integers?
4. Could there be other constraints we missed in the puzzle?
5. How might the given numbers 13 and 8 relate to the final solution?

**Tip:** When solving puzzles with multiple unknowns, it's helpful to look for relationships between the equations to reduce free variables.

The puzzle shows a grid of equations with some yellow squares that need to be filled in. The first row is two yellow squares added together equals 8. The second row is two yellow squares added together equals 6. The third row is one yellow square minus another equals 13. The goal is to find the values of the yellow squares that satisfy all the conditions.

This puzzle involves solving a system of linear equations using addition and subtraction. Discover how to find the values of unknowns represented by yellow squares in the grid, where the sum of two unknowns equals 8, another pair equals 6, and the difference equals 13. Perfect for students in Grades 6-8.

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