Answer
$x=\dfrac{1}{5}, y = \dfrac{3}{10} \text{ or } \left(\dfrac{1}{5}, \dfrac{3}{10}\right)$
Work Step by Step
The system of equations is given by the following two equations:
$$\begin{cases}
3x-2y=0\hspace{20pt} (1)\\[3mm]
5x+10y=4 \hspace{20pt} (2)
\end{cases}$$
Multiplying equation $(1)$ by $5$ so that the coefficients of y in the two equations are additive inverses gives:
$15x-10y=0\hspace{20pt} (1)$
$\text{Add the two equations to eliminate } y$:
\[
\begin{aligned} 15x-10y&=0 \\[2mm]
5x+10y&=4 \ \\[3mm]
\hline 20x&=4\\[2mm]
\end{aligned}
\]
Divdei both sides by $20$ to obtain:
$x=\dfrac{4}{20}$
$x=\dfrac{1}{5}$
$\text{Substituting in equation (2) for }x=\dfrac{1}{5}$ gives:
$5\left(\dfrac{1}{5} \right)+10y = 4$
$1+10y=4$
$10y = 3$
$y = \dfrac{3}{10}$
Therefore, the solution is:
$\boxed{x=\dfrac{1}{5} \hspace{20pt} y = \dfrac{3}{10}}$
