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The image contains a problem asking to solve for the variable \( a \) given a system of equations, particularly in matrix form.

The problem provides a \( 2 \times 2 \) matrix equation, which likely needs to be equated to another matrix. Unfortunately, the content is slightly blurry, but I can help solve it if I can make out the numbers and expressions.

The matrix equation looks like:

\[
\begin{pmatrix}
1 & a \\
3 & 2
\end{pmatrix}
\begin{pmatrix}
x \\
y
\end{pmatrix}
= 
\begin{pmatrix}
3 \\
5
\end{pmatrix}
\]

If that is the correct reading, you solve for \( a \) by solving the system of linear equations derived from the matrix multiplication.

1. **Extract the system of equations**:
   - \( 1 \cdot x + a \cdot y = 3 \)
   - \( 3 \cdot x + 2 \cdot y = 5 \)

2. **Solve the system for \( x \) and \( y \)**:
   From the second equation, express \( x \) in terms of \( y \):
   \[
   x = \frac{5 - 2y}{3}
   \]
   
   Substitute \( x \) in the first equation:
   \[
   1 \cdot \frac{5 - 2y}{3} + a \cdot y = 3
   \]

3. **Solve the equation**:
   Multiply the entire equation by 3 to eliminate the fraction:
   \[
   5 - 2y + 3ay = 9
   \]
   Combine like terms:
   \[
   3ay - 2y = 4
   \]
   Factor out \( y \):
   \[
   y(3a - 2) = 4
   \]

4. **Find \( y \)**:
   \[
   y = \frac{4}{3a - 2}
   \]
   
   Substitute \( y \) back into one of the original equations to solve for \( a \). However, you also need to solve the system simultaneously. This process involves some algebraic manipulation.

Do you want me to continue with these calculations? Please confirm if the matrix and the resulting system are as I interpreted or provide more details if they differ.

Learn how to solve for the variable a in a matrix equation with a detailed step-by-step solution. This problem involves matrix algebra and systems of linear equations, focusing on matrix multiplication. Suitable for students in Grades 10-12.

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