Question

If $\left[\begin{array}{cc}x& x-y\\ 2x+y& 7\end{array}\right]=\left[\begin{array}{cc}3& 1\\ 8& 7\end{array}\right]$, then find the value of y.

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{have},\left[\begin{array}{cc}x& x-y\\ 2x+y& 7\end{array}\right]=\left[\begin{array}{cc}3& 1\\ 8& 7\end{array}\right] \\ \mathrm{The}\mathrm{corresponding}\mathrm{elements}\mathrm{of}\mathrm{two}\mathrm{equal}\mathrm{matrices}\mathrm{are}\mathrm{equal}. \\ \therefore x=3 \\ x-y=1...\left(1\right) \\ \mathrm{Putting}\mathrm{the}\mathrm{value}\mathrm{of}x\mathrm{in}\mathrm{eq}.\left(1\right) \\ 3-y=1 \\ \Rightarrow 3-1=y \\ \therefore y=2 \end{gathered}$$