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