Answer
$[x]_B=\begin{bmatrix}
7\\
5\\
\end{bmatrix}
$
Work Step by Step
We can calculate the B coordinate vector of x by row reducing the augmented matrix
$\begin{bmatrix}
1&-2&-3\\
-4&7&7\\
\end{bmatrix}
$~$\begin{bmatrix}
1&0&7\\
0&1&5\\
\end{bmatrix}$
$[x]_B=\begin{bmatrix}
7\\
5\\
\end{bmatrix}
$
