https://file.aiquickdraw.com/mathbot/file/17258481025585t60gyqi.jpg

Let me analyze the image for you to extract the mathematical content and provide solutions.

Please give me a moment.From the image provided, it appears to be a math puzzle labeled "Puzzle #6" with multiple equations and an answer choice table. There are four sticky notes with different expressions, which seem to provide clues. I'll extract and solve the individual puzzles, one by one, as shown.

### Clue 1 (Purple):
\[
2x + y = 6, \quad x - y = 1
\]
This is a system of linear equations. To solve it:

1. Solve \( x - y = 1 \) for \( x \):
   \[
   x = y + 1
   \]
2. Substitute \( x = y + 1 \) into \( 2x + y = 6 \):
   \[
   2(y + 1) + y = 6
   \]
   Simplify:
   \[
   2y + 2 + y = 6 \quad \Rightarrow \quad 3y + 2 = 6
   \]
   Solve for \( y \):
   \[
   3y = 4 \quad \Rightarrow \quad y = \frac{4}{3}
   \]
3. Now, substitute \( y = \frac{4}{3} \) into \( x = y + 1 \):
   \[
   x = \frac{4}{3} + 1 = \frac{7}{3}
   \]
   Thus, the solution is \( x = \frac{7}{3}, y = \frac{4}{3} \).

Now, I'll move to the next clues.

### Clue 2 (Yellow):
It appears to show an expression involving square roots.

### Clue 3 (Green):
This seems to be another equation, but I need more details to solve each. Would you like me to continue extracting the math or expand on one of the clues?

Based on the query submitted by the user and the corresponding solution, generate the following information in JSON format.

Learn how to solve a math puzzle involving systems of linear equations and quadratic equations. This problem covers key algebraic concepts, including linear combination and substitution methods, and the quadratic formula theorem. Suitable for students in Grades 9-12.

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