Answer
\[x=-5\;,\; y=9\]
Work Step by Step
\[2x+y=-1\\
5x+3y=2\]
Here $\;\;A=\left[\begin{array}{cc}
2&1\\
5&3
\end{array}\right] \;\;,b=\left[\begin{array}{c}
-1\\
2\end{array}\right]$
And $\;\;X=\left[\begin{array}{c}
x\\
y\end{array}\right]$
Consider $\;\;A=\left[\begin{array}{cc}
2&1\\
5&3
\end{array}\right]$
Here $\;2(3)-1(5)=1\neq 0$
$\Rightarrow A$ is invertible
$A^{-1}=\frac{1}{6-5}\left[\begin{array}{cc}
3&-1\\
-5&2
\end{array}\right]$
$\Rightarrow A^{-1}=\left[\begin{array}{cc}
3&-1\\
-5&2
\end{array}\right]$
$X=A^{-1}b$
$X=\left[\begin{array}{cc}
3&-1\\
-5&2
\end{array}\right]\left[\begin{array}{c}
-1\\
2\end{array}\right]$
$\Rightarrow X=\left[\begin{array}{c}
-3-2\\
5+4\end{array}\right]$
$\Rightarrow X=\left[\begin{array}{c}
-5\\
9\end{array}\right]$
$\Rightarrow \left[\begin{array}{c}
x\\
y\end{array}\right] =\left[\begin{array}{c}
-5\\
9\end{array}\right]$
$\Rightarrow x=-5\:,\;y=9$
Hence $x=-5\:,\;y=9$.
