Question

Find the value of $x+y$ from the following equation:
$2\left[\begin{array}{cc}x& 5\\ 7& y-3\end{array}\right]+\left[\begin{array}{cc}3& -4\\ 1& 2\end{array}\right]=\left[\begin{array}{cc}7& 6\\ 15& 14\end{array}\right]$

Answer 1

Consider $2\left[\begin{array}{cc}x& 5\\ 7& y-3\end{array}\right]+\left[\begin{array}{cc}3& -4\\ 1& 2\end{array}\right]=\left[\begin{array}{cc}7& 6\\ 15& 14\end{array}\right]$ as shown below:

$\left[\begin{array}{cc}2x& 10\\ 14& 2y-6\end{array}\right]+\left[\begin{array}{cc}3& -4\\ 1& 2\end{array}\right]=\left[\begin{array}{cc}7& 6\\ 15& 14\end{array}\right]$

$\left[\begin{array}{cc}2x+3& 10-4\\ 14+1& 2y-6+2\end{array}\right]=\left[\begin{array}{cc}7& 6\\ 15& 14\end{array}\right]$

$\left[\begin{array}{cc}2x+3& 6\\ 15& 2y-4\end{array}\right]=\left[\begin{array}{cc}7& 6\\ 15& 14\end{array}\right]$

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

$2x+3=7⟹2x=4⟹x=2$

$2y-4=14⟹2y=18⟹y=9$

Hence $x+y=2+9=11$.