Answer
$1$
Work Step by Step
ٍSince $x=2u+v$ and $y=5u+3v$, we solve them for $u$ and $v$ and we get $u=3x-y$ and $v=-5x+2y.$ Now we have $G^{-1}(x,y)=(3x-y,-5x+2y)$ and hence
$$
\operatorname{Jac}(G^{-1})=\frac{\partial(u,v)}{\partial(x, y)}=\left|\begin{array}{ll}
{\frac{\partial u}{\partial x}} & {\frac{\partial u}{\partial y}} \\
{\frac{\partial v}{\partial x}} & {\frac{\partial x}{\partial x}}
\end{array}\right| =\left|\begin{array}{ll}
{ 3} & {-1} \\
{-5} & {2}
\end{array}\right| =6-5=1.
$$
