# Solve this following

Question:

If $\left[\begin{array}{cc}x-y & 2 y \\ 2 y+z & x+y\end{array}\right]=\left[\begin{array}{ll}1 & 4 \\ 9 & 5\end{array}\right]$ then write the value of $(x+y)$.

Solution:

If $\left[\begin{array}{ll}a & b \\ c & d\end{array}\right]=\left[\begin{array}{ll}e & f \\ g & h\end{array}\right]$

Then $a=e, b=f, c=g, d=h$

Given, $\left[\begin{array}{cc}x-y & 2 y \\ 2 y+z & x+y\end{array}\right]=\left[\begin{array}{cc}1 & 4 \\ 9 & 5\end{array}\right]$

So, $x-y=1, x+y=5,2 y=4$ and $2 y+z=9$

Therefore, $x+y=5$

Conclusion: $x+y=5$