Answer
$y=\begin{bmatrix}
1\\
5\\
1\\
-3\\
\end{bmatrix}$, $x=\begin{bmatrix}
-2\\
-1\\
2\\
-3\\
\end{bmatrix}$
Work Step by Step
$Ax=b$
$LUx=b$
First, row reduce the augmented matrix $[L\ b]$ to calculate $Ux$.
$\begin{bmatrix}
1&0&0&0&1\\
2&1&0&0&7\\
-1&0&1&0&0\\
-4&3&-5&1&3\\
\end{bmatrix}$
$y=Ux=\begin{bmatrix}
1\\
5\\
1\\
-3\\
\end{bmatrix}$
Next, row reduce augmented matrix $[Uy]$ to calculate $x$.
$\begin{bmatrix}
1&-2&-4&-3&1\\
0&-3&1&0&5\\
0&0&2&1&1\\
0&0&0&1&-3\\
\end{bmatrix}$
$x=\begin{bmatrix}
-2\\
-1\\
2\\
-3\\
\end{bmatrix}$
