Answer
$[x]_B=\begin{bmatrix}
1/4\\
-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&4\\
5&-7&10\\
-3&5&-7
\end{bmatrix}
$~$\begin{bmatrix}
1&0&1/4\\
0&1&-5/4\\
0&0&0
\end{bmatrix}$
$[x]_B=\begin{bmatrix}
1/4\\
-5/4\\
\end{bmatrix}
$
