https://file.aiquickdraw.com/mathbot/file/1725377015131xxyppaj0.jpg

The image shows a system of linear equations:

\[
\begin{cases}
5x + 2y = 1 \\
3x + 2y = 3
\end{cases}
\]

To solve this system, we can use the elimination method. Here's the step-by-step process:

1. **Subtract the second equation from the first** to eliminate \(2y\):

   \[
   (5x + 2y) - (3x + 2y) = 1 - 3
   \]

   Simplifying this, we get:

   \[
   2x = -2
   \]

2. **Solve for \(x\)**:

   \[
   x = \frac{-2}{2} = -1
   \]

3. **Substitute \(x = -1\) into the first equation** to solve for \(y\):

   \[
   5(-1) + 2y = 1
   \]

   Simplify this equation:

   \[
   -5 + 2y = 1
   \]

   Add 5 to both sides:

   \[
   2y = 6
   \]

4. **Solve for \(y\)**:

   \[
   y = \frac{6}{2} = 3
   \]

**Solution**: \(x = -1\) and \(y = 3\).

Would you like a more detailed explanation of any of these steps, or do you have any questions?

### Related Questions:
1. How can you solve the system using substitution?
2. What are other methods to solve a system of equations?
3. Can a system of equations have no solution?
4. How do you graphically interpret the solution \((x, y)\)?
5. How do you verify the solution is correct?

**Tip:** When using elimination, always double-check that the coefficients of one variable are aligned correctly to simplify the elimination process efficiently.

Solve the system of equations: 5x + 2y = 1 and 3x + 2y = 3.

Learn how to solve the system of linear equations 5x + 2y = 1 and 3x + 2y = 3 using the elimination method. This detailed solution is suitable for students in Grades 8-10 and covers key algebraic concepts.

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