Question

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 $x+y=$

• (A) 3
• (B) 4
• (C) 5
• (D) 6

Answer 1

The Correct Option is C

Explanation:
As we know,When two matrices are equal, all the corresponding elements must be equal.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 two elements of first column,$2x+y=7$$\Rightarrow y=7-2x$...(1)$5x-7=y$...(2)Compairing value of $y$ from equation (1) and (2) we get,$7-2x=5x-7$$\Rightarrow 7+7=5x+2x$$\Rightarrow 14=7x$$\therefore x=2$Putting value of $x$ in equation (1), we get$y=7-2\times 2$$\Rightarrow y=7-4$$\Rightarrow y=3$Now, $x+y=2+3=5$So, the value of $x+y$ is $5$.Hence, the correct option is (C).