Answer
$x=1\quad y=-2$
Work Step by Step
Matrices are equal if they have the same dimension and
all the corresponding entries are equal.
$2\left[\begin{array}{cc}
x & y\\
x+y & x-y
\end{array}\right]=\left[\begin{array}{cc}
2x & 2y\\
2x+2y & 2x-2y
\end{array}\right]$
$\left[\begin{array}{cc}
2x & 2y\\
2x+2y & 2x-2y
\end{array}\right]$=$\left[\begin{array}{rrr}
2 & -4\\
-2 & 6
\end{array}\right]$
$a_{11}\Rightarrow\quad 2x=2\Rightarrow\quad x=1$
$a_{12}\Rightarrow\quad 2y=-4\Rightarrow\quad y=-2$
Checking at $a_{21},$
$2(1)+2(-2)=-2$
Checking at $a_{22},$
$2(1)-2(-2)=6$
$x=1\quad y=-2$
