Answer
$T^{-1}(x_1,x_2)=(3.5x_1+4x_2, 2.5x_1+3x_2)$
Work Step by Step
The standard matrix of T is $\begin{bmatrix}
T(e1)&T(e_2)\\
\end{bmatrix}
$ where $T(e1)=\begin{bmatrix}
6\\-5\\
\end{bmatrix}$ and $T(e2)=\begin{bmatrix}
-8\\7\\
\end{bmatrix}$
The standard matrix of T is $\begin{bmatrix}
6&-8\\-5&7\\
\end{bmatrix}
$ and its determinant is $2$, so its inverse is $\begin{bmatrix}
3.5&4\\2.5&3\\
\end{bmatrix}
$
$T^{-1}(x_1,x_2)=(3.5x_1+4x_2, 2.5x_1+3x_2)$
