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 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

Answer 1

$$\begin{gathered} \left[\begin{array}{cc}2x+y& 4x\\ 5x-7& 4x\end{array}\right]=\left[\begin{array}{cc}7& 7y-13\\ y& x+6\end{array}\right] \\ \mathrm{Corresponding}\mathrm{elements}\mathrm{of}\mathrm{equal}\mathrm{matrices}\mathrm{are}\mathrm{equal}. \\ \therefore 4x=x+6\mathrm{and}2x+y=7 \\ \Rightarrow 3x=6\mathrm{and}2x+y=7 \\ \Rightarrow x=2\mathrm{and}2x+y=7 \\ \Rightarrow x=2\mathrm{and}2\times 2+y=7 \\ \Rightarrow x=2\mathrm{and}y=7-4 \\ \Rightarrow x=2\mathrm{and}y=3 \end{gathered}$$

Therefore, x = 2, y = 3.

Hence, the correct option is (b).