If $\begin{bmatrix$}[r] 5 & 2 \ -1 & y + 1 \end{bmatrix} - 2\begin{bmatrix}[r] 1 & 2x - 1 \ 3 & -2 \end{bmatrix} = \begin{bmatrix}[r] 3 & -8 \ -7 & 2 \end{bmatrix}, find the values of x and y.

Given,

$\Rightarrow \begin{bmatrix$}[r] 5 & 2 \ -1 & y + 1 \end{bmatrix} - 2\begin{bmatrix}[r] 1 & 2x - 1 \ 3 & -2 \end{bmatrix} = \begin{bmatrix}[r] 3 & -8 \ -7 & 2 \end{bmatrix} \\[1em] \Rightarrow \begin{bmatrix}[r] 5 & 2 \ -1 & y + 1 \end{bmatrix} - \begin{bmatrix}[r] 2 & 4x - 2 \ 6 & -4 \end{bmatrix} = \begin{bmatrix}[r] 3 & -8 \ -7 & 2 \end{bmatrix} \\[1em] \Rightarrow \begin{bmatrix}[r] 5 - 2 & 2 - 4x + 2 \ -1 - 6 & y + 1 - (-4) \end{bmatrix} = \begin{bmatrix}[r] 3 & -8 \ -7 & 2 \end{bmatrix} \\[1em] \Rightarrow \begin{bmatrix}[r] 3 & 4 - 4x \ -7 & y + 5 \end{bmatrix} = \begin{bmatrix}[r] 3 & -8 \ -7 & 2 \end{bmatrix} \\[1em] \Rightarrow 4 - 4x = -8 \text{ and } y + 5 = 2 \\[0.5em] \Rightarrow 4x = 8 + 4 \text{ and } y = 2 - 5 \\[0.5em] \Rightarrow 4x = 12 \text{ and } y = -3 \\[0.5em]

∴ x = 3 and y = -3.

Hence, the value of x = 3 and y = -3.