Answer
$(\displaystyle \frac{1}{5},\frac{3}{10})$
Work Step by Step
Cramer's rule
$\left\{\begin{array}{l}{a x+b y=s}\\{cx+dy=t}\end{array}\right.$
$D=\left|\begin{array}{ll}{a}&{b}\\{c}&{d}\end{array}\right|,D_{x}=\left|\begin{array}{ll}{s}&{b}\\{t}&{d}\end{array}\right|,D_{y}=\left|\begin{array}{ll}{a}&{s}\\{c}&{t}\end{array}\right|,$
If $D\displaystyle \neq 0,\qquad x=\frac{D_{x}}{D}\quad y=\frac{D_{y}}{D}$
---
$\left\{\begin{array}{l}{3 x-2 y=0}\\{5x+10y=4}\end{array}\right.\Rightarrow\left[\begin{array}{ll}
a & b\\
c & d
\end{array}\right]=\left[\begin{array}{ll}
3 & -2\\
5 & 10
\end{array}\right],\quad \left[\begin{array}{l}
s\\
t
\end{array}\right]=\left[\begin{array}{l}
0\\
4
\end{array}\right]$
$\begin{array}{lllll}
D=\left|\begin{array}{ll}
3 & -2\\
5 & 10
\end{array}\right|= & & D_{x}=\left|\begin{array}{ll}
0 & -2\\
4 & 10
\end{array}\right|= & & D_{y}=\left|\begin{array}{ll}
3 & 0\\
5 & 4
\end{array}\right|=\\
=30+10 & & =0+8 & & =12-0\\
=40\neq 0 & & =8 & & =12\\
& & & &
\end{array}$
$x=\displaystyle \frac{D_{x}}{D}=\frac{8}{40}=\frac{1}{5}$
$y=\displaystyle \frac{D_{y}}{D}=\frac{12}{40}=\frac{3}{10}$
Solution: $(x,y)=(\displaystyle \frac{1}{5},\frac{3}{10})$