Question

Find the value of $x+y$ from the following equation:
$2(\begin{array}{cc}1& 3\\ 0& x\end{array})+(\begin{array}{cc}y& 0\\ 1& 2\end{array})=(\begin{array}{cc}5& 6\\ 1& 8\end{array})$

Answer 1

Consider,

$2\left(\begin{array}{cc}1& 3\\ 0& x\end{array}\right)+\left(\begin{array}{cc}y& 0\\ 1& 2\end{array}\right)=\left(\begin{array}{cc}5& 6\\ 1& 8\end{array}\right)$

$\left(\begin{array}{cc}2& 6\\ 0& 2x\end{array}\right)+\left(\begin{array}{cc}y& 0\\ 1& 2\end{array}\right)=\left(\begin{array}{cc}5& 6\\ 1& 8\end{array}\right)$

$\left(\begin{array}{cc}2+y& 6+0\\ 0+1& 2x+2\end{array}\right)=\left(\begin{array}{cc}5& 6\\ 1& 8\end{array}\right)$

$\left(\begin{array}{cc}2+y& 6\\ 1& 2x+2\end{array}\right)=\left(\begin{array}{cc}5& 6\\ 1& 8\end{array}\right)$

Equating the matrices we get the values of $x$ and $y$ as follows:

$2+y=5⟹y=3$

$2x+2=8⟹2x=6⟹x=3$

Therefore, $x+y=3+3=6$

Hence $x+y=6$.