If $2\begin{bmatrix$}[r] x & 7 \ 9 & y - 5 \end{bmatrix} + \begin{bmatrix}[r] 6 & -7 \ 4 & 5 \end{bmatrix} = \begin{bmatrix}[r] 10 & 7 \ 22 & 15 \end{bmatrix}, find the values of x and y.

Given,

$\Rightarrow 2\begin{bmatrix$}[r] x & 7 \ 9 & y - 5 \end{bmatrix} + \begin{bmatrix}[r] 6 & -7 \ 4 & 5 \end{bmatrix} = \begin{bmatrix}[r] 10 & 7 \ 22 & 15 \end{bmatrix} \\[1em] \Rightarrow \begin{bmatrix}[r] 2x & 14 \ 18 & 2y - 10 \end{bmatrix} + \begin{bmatrix}[r] 6 & -7 \ 4 & 5 \end{bmatrix} = \begin{bmatrix}[r] 10 & 7 \ 22 & 15 \end{bmatrix} \\[1em] \Rightarrow \begin{bmatrix}[r] 2x + 6 & 14 + (-7) \ 18 + 4 & 2y - 10 + 5 \end{bmatrix} = \begin{bmatrix}[r] 10 & 7 \ 22 & 15 \end{bmatrix} \\[1em] \Rightarrow 2x + 6 = 10 \text{ and } 2y - 5 = 15 \\[1em] \Rightarrow 2x = 4 \text{ and } 2y = 20 \\[1em]

∴ x = 2 and y = 10.

Hence, the value of x = 2 and y = 10.