https://file.aiquickdraw.com/mathbot/file/1725632212840mgwhs7i8.jpg

From the image, the system of equations appears to be:

\[
\frac{2x^3 + 3y^2}{y} = \frac{5}{6}
\]

\[
\frac{2x^5 - 3y^3}{x} = \frac{1}{12}
\]

I can solve this system of equations for \(x\) and \(y\) step-by-step. Let me first simplify both equations.

1. Multiply both sides of the first equation by \(y\) to eliminate the denominator:

\[
2x^3 + 3y^2 = \frac{5}{6} y
\]

2. Multiply both sides of the second equation by \(x\) to eliminate the denominator:

\[
2x^5 - 3y^3 = \frac{1}{12} x
\]

Now I'll proceed with solving this system.The only solution to the given system of equations is \( x = 0 \) and \( y = 0 \). 

Would you like further clarification or a deeper analysis of this solution?

Here are 5 related questions to expand your understanding:
1. How would the system change if the constants on the right side were different?
2. What would happen if either \(x\) or \(y\) were restricted to non-zero values?
3. How can you verify solutions to non-linear systems of equations?
4. What are the methods to solve such systems when more than one solution exists?
5. How does the degree of the variables affect the complexity of solving equations?

**Tip**: Always verify your solution by substituting it back into the original equations to ensure they satisfy both equations.

Solve the system of equations:
(2x^3 + 3y^2) / y = 5/6
(2x^5 - 3y^3) / x = 1/12

Learn how to solve a system of non-linear equations, such as (2x^3 + 3y^2)/y = 5/6 and (2x^5 - 3y^3)/x = 1/12. This solution includes simplifying the equations and finding that x = 0 and y = 0 is the only solution. Suitable for students in Grades 9-12.

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