Find x

Given:

\[ \begin{bmatrix} 3x + y & -y \\ 2y – x & 3 \end{bmatrix} = \begin{bmatrix} 1 & 2 \\ -5 & 3 \end{bmatrix} \]

Step 1: Compare Elements

\[ -y = 2 \Rightarrow y = -2 \]

\[ 2y – x = -5 \]

Step 2: Substitute y

\[ 2(-2) – x = -5 \Rightarrow -4 – x = -5 \]

\[ -x = -1 \Rightarrow x = 1 \]

Verification:

\[ 3x + y = 3(1) + (-2) = 1 \quad (\text{correct}) \]

Final Answer:

\[ x = 1 \]