Question

Solve for $x$ and $y$:

$2\left[\begin{array}{cc}x& 7\\ 9& y-5\end{array}\right]+\left[\begin{array}{cc}6& -7\\ 4& 5\end{array}\right]=\left[\begin{array}{cc}10& 7\\ 22& 15\end{array}\right]$

Answer 1

for given matrices.
$\left[\begin{array}{cc}2x& 14\\ 18& 2y-10\end{array}\right]$ +$\left[\begin{array}{cc}6& -7\\ 4& 5\end{array}\right]$=$\left[\begin{array}{cc}10& 7\\ 22& 15\end{array}\right]$
Adding matrices on L.H.S.,
$\left[\begin{array}{cc}2x+6& 7\\ 22& 2y-5\end{array}\right]$=$\left[\begin{array}{cc}10& 7\\ 22& 15\end{array}\right]$
On comparing elements of matrices on both side,
=>$2x+6=10$.................(1)
=>$2y-5=15$ ................(2)
from (1) and (2),
$x=2andy=10$