Question
Find $x$ and $y$, if $\left[\begin{array}{ccc}2 x+y & -1 & 1 \\ 3 & 4 y & 4\end{array}\right]+\left[\begin{array}{ccc}-1 & 6 & 4 \\ 3 & 0 & 3\end{array}\right]=\left[\begin{array}{ccc}3 & 5 & 5 \\ 6 & 18 & 7\end{array}\right]$
$\therefore \quad\left[\begin{array}{ccc}2 x+y-1 & -1+6 & 1+4 \\ 3+3 & 4 y+0 & 4+3\end{array}\right]=\left[\begin{array}{ccc}3 & 5 & 5 \\ 6 & 18 & 7\end{array}\right]$
$\therefore \quad\left[\begin{array}{ccc}2 x+y-1 & 5 & 5 \\ 6 & 4 y & 7\end{array}\right]=\left[\begin{array}{ccc}3 & 5 & 5 \\ 6 & 18 & 7\end{array}\right]$
∴ By equality of matrices, we get 2x + y – 1 = 3 and 4y = 18
$\begin{aligned} & \therefore 2 x+y=4 \text { and } y=\frac{18}{4}=\frac{9}{2} \\ & \therefore 2 x+\frac{9}{2}=4 \\ & \therefore 2 x=4-\frac{9}{2} \\ & \therefore 2 x=\frac{1}{2}= \\ & \therefore x=-\frac{1}{4}=\text { and } y=\frac{9}{2}=\end{aligned}$
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