Question

If 2$\left[\begin{array}{cc}3& 4\\ 5& x\end{array}\right]+\left[\begin{array}{cc}1& y\\ 0& 1\end{array}\right]=\left[\begin{array}{cc}7& 0\\ 10& 5\end{array}\right]$, find x and y.

Answer 1

$$\begin{gathered} \mathrm{Given}:\hspace{0.17em}2\left[\begin{array}{cc}3& 4\\ 5& x\end{array}\right]+\left[\begin{array}{cc}1& y\\ 0& 1\end{array}\right]=\left[\begin{array}{cc}7& 0\\ 10& 5\end{array}\right] \\ \Rightarrow \left[\begin{array}{cc}6& 8\\ 10& 2x\end{array}\right]+\left[\begin{array}{cc}1& y\\ 0& 1\end{array}\right]=\left[\begin{array}{cc}7& 0\\ 10& 5\end{array}\right] \\ \Rightarrow \left[\begin{array}{cc}6+1& 8+y\\ 10+0& 2x+1\end{array}\right]=\left[\begin{array}{cc}7& 0\\ 10& 5\end{array}\right] \\ \Rightarrow \left[\begin{array}{cc}7& 8+y\\ 10& 2x+1\end{array}\right]=\left[\begin{array}{cc}7& 0\\ 10& 5\end{array}\right] \\ \therefore 8+y=0 \\ \Rightarrow y=-8 \\ \mathrm{Also}, \\ 2x+1=5 \\ \Rightarrow 2x=4 \\ \Rightarrow x=\frac{4}{2}=2 \\ \therefore x=2\mathrm{and}y=-8 \end{gathered}$$