https://file.aiquickdraw.com/mathbot/file/1725785511541heh8c3s1.jpg

The image you uploaded contains a system of equations that need to be solved. Here's the system of equations from the image:

\[
\begin{aligned}
2x + 3y &= 1, \\
3x - 2y &= 11.
\end{aligned}
\]

### Solving the System

We can solve this system using either substitution or elimination. I'll use the elimination method.

1. **Multiply the equations to eliminate one variable:**

   - Multiply the first equation by 2:
     \[
     4x + 6y = 2
     \]
   - Multiply the second equation by 3:
     \[
     9x - 6y = 33
     \]

2. **Add the two equations to eliminate \( y \):**
   \[
   (4x + 6y) + (9x - 6y) = 2 + 33
   \]
   \[
   13x = 35
   \]
   \[
   x = \frac{35}{13}
   \]

3. **Substitute \( x \) back into one of the original equations to solve for \( y \):**
   \[
   2\left(\frac{35}{13}\right) + 3y = 1
   \]
   \[
   \frac{70}{13} + 3y = 1
   \]
   \[
   3y = 1 - \frac{70}{13} = \frac{13}{13} - \frac{70}{13} = \frac{-57}{13}
   \]
   \[
   y = \frac{-57}{39} = \frac{-19}{13}
   \]

### Solution

So, the solution to the system is:
\[
x = \frac{35}{13}, \quad y = \frac{-19}{13}
\]

If you enter your answer in the form \( x, y \), it should be:
\[
\left(\frac{35}{13}, \frac{-19}{13}\right)
\]

Would you like more details or have any questions about this solution?

Here are some related questions:
1. How would you solve the system using the substitution method?
2. What would the solution be if you used matrix methods (e.g., Gaussian elimination)?
3. How do you interpret the solution of a system of equations graphically?
4. Could you explain what happens if a system of equations has no solution or infinitely many solutions?
5. What are some real-world applications of solving systems of equations?

**Tip:** When solving systems of equations, always double-check your work by substituting your solution back into the original equations to ensure they satisfy both equations.

Find the solution to the system of equations: 2x + 3y = 1, 3x - 2y = 11.

Learn how to solve the system of linear equations 2x + 3y = 1 and 3x - 2y = 11 using the elimination method. This problem covers key algebraic concepts like solving systems of equations and finding the solution using elimination. Suitable for high school students (Grades 9-12).

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