If $\left[\begin{array}{cc}2 x+y & 4 x \\ 5 x-7 & 4 x\end{array}\right]=\left[\begin{array}{cc}7 & 7 y-13 \\ y & x+6\end{array}\right]$, then the value of $x$ and $y$ is
(a) $x=3, y=1$
(b) $x=2, y=3$
(c) $x=2, y=4$
(d) $x=3, y=3$
$\left[\begin{array}{cc}2 x+y & 4 x \\ 5 x-7 & 4 x\end{array}\right]=\left[\begin{array}{cc}7 & 7 y-13 \\ y & x+6\end{array}\right]$
Corresponding elements of equal matrices are equal.
$\therefore 4 x=x+6 \quad$ and $\quad 2 x+y=7$
$\Rightarrow 3 x=6 \quad$ and $\quad 2 x+y=7$
$\Rightarrow x=2 \quad$ and $\quad 2 x+y=7$
$\Rightarrow x=2 \quad$ and $\quad 2 \times 2+y=7$
$\Rightarrow x=2 \quad$ and $\quad y=7-4$
$\Rightarrow x=2 \quad$ and $\quad y=3$
Therefore, $x=2, y=3$.
Hence, the correct option is (b).
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