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