Question

$\text{If}\left[\begin{array}{cc}2x+y& 4x\\ 5x-7& 4x\end{array}\right]=\left[\begin{array}{cc}7& 7y-13\\ y& x+6\end{array}\right]$ then the value of $x,y$ is,

• A. $x=3;y=3$
• B. $x=2;y=4$
• C. $x=3;y=1$
• D. $x=2;y=3$

Answer 1

The correct option is D $x=2;y=3$

$\text{Given}\left[\begin{array}{cc}2x+y& 4x\\ 5x-7& 4x\end{array}\right]=\left[\begin{array}{cc}7& 7y-13\\ y& x+6\end{array}\right]$
Comparing the corresponding elements, we get
$4x=x+6$
$\Rightarrow 3x=6$
$\Rightarrow x=2$
$2x+y=7$
$\Rightarrow y=7-2x$
$\Rightarrow y=7-4$
$\Rightarrow y=3$
Hence, the value of $x,y$ are $2,3$ respectively.
So option (b) is correct.