Question

Find the value of $y-x$ 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

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

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

Therefore,

$2x+3=7⟹x=2$

And, $2y-4=14⟹y=9$

Hence, $y-x=9-2=7$