# Find the values of x and y,

Question:

Find the values of $x$ and $y$, if $2\left[\begin{array}{ll}1 & 3 \\ 0 & x\end{array}\right]+\left[\begin{array}{ll}y & 0 \\ 1 & 2\end{array}\right]=\left[\begin{array}{ll}5 & 6 \\ 1 & 8\end{array}\right]$

Solution:

Given : $2\left[\begin{array}{ll}1 & 3 \\ 0 & x\end{array}\right]+\left[\begin{array}{ll}y & 0 \\ 1 & 2\end{array}\right]=\left[\begin{array}{ll}5 & 6 \\ 1 & 8\end{array}\right]$

$\Rightarrow\left[\begin{array}{cc}2 & 6 \\ 0 & 2 x\end{array}\right]+\left[\begin{array}{ll}y & 0 \\ 1 & 2\end{array}\right]=\left[\begin{array}{ll}5 & 6 \\ 1 & 8\end{array}\right]$

$\Rightarrow\left[\begin{array}{cc}2+y & 6+0 \\ 0+1 & 2 x+2\end{array}\right]=\left[\begin{array}{ll}5 & 6 \\ 1 & 8\end{array}\right]$

$\Rightarrow\left[\begin{array}{cc}2+y & 6 \\ 1 & 2 x+2\end{array}\right]=\left[\begin{array}{ll}5 & 6 \\ 1 & 8\end{array}\right]$

$\therefore 2+y=5$ and $2 x+2=8$

$\Rightarrow y=5-2$ and $2 x=8-2$

$\Rightarrow y=3$ and $2 x=6$

$\Rightarrow x=\frac{6}{2}=3$