If \(2\begin{bmatrix}3 & 4\\5 & x\end{bmatrix}+\begin{bmatrix}1 & y\\0 & 1\end{bmatrix}=\begin{bmatrix}7 & 0\\10 & 5\end{bmatrix}\), then the value of x - y is:

10

\(2\begin{bmatrix}3 & 4\\5 & x\end{bmatrix}=\begin{bmatrix}6 & 8\\10 & 2x\end{bmatrix}\)  ...(i)

According to questions,

$\begin{bmatrix}6 & 8\\10 & 2x\end{bmatrix}+\begin{bmatrix}1 & y\\0 & 1\end{bmatrix}=\begin{bmatrix}7 & 0\\10 & 5\end{bmatrix}$ from eq. (i)

$\begin{bmatrix}7 & 8+y\\10 & 2x+1\end{bmatrix}$

⇒ 8 + y = 0

y = 0 - 8

y = -8

and 2x + 1= 5

2x = 5 - 1 = 4

2x = 4

$x = \frac{4}{2}=2⇒x=2$

So, value of x - y = 2 - (-8) = 10