The numerical solution to the system of equations is approximately:

\[
\begin{aligned}
p &\approx 0.9761 \\
q &\approx 0.9755 \\
x &\approx 0.9730 \\
y &\approx 0.9744 \\
\end{aligned}
\]

These values satisfy the system within the limits of numerical accuracy.

Would you like to explore any further details, or have any questions? Here are some related questions you might find interesting:

1. How are numerical methods like `fsolve` used in more complex systems?
2. What are the limitations of numerical methods compared to algebraic solutions?
3. How can we verify the accuracy of numerical solutions?
4. What are other methods for solving systems of nonlinear equations?
5. How can this system be interpreted geometrically?
6. What are some real-world applications of solving such systems of equations?
7. How would the solution change if the coefficients in the equations were slightly altered?
8. What are some challenges in solving systems with more variables or equations?

**Tip:** Always check the consistency and the nature of your system before proceeding with solving, as this can help in choosing the most appropriate method.

Explore numerical methods for solving systems of equations with an example solution. Learn about numerical accuracy and practical applications. Suitable for advanced high school and college-level students.

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