Answer
$\left\{\left(\dfrac{1}{5},\dfrac{3}{10}\right)\right\}$
Work Step by Step
We are given the system of equations:
$\begin{cases}
3x-2y=0\\
5x+10y=4
\end{cases}$
Use the elimination method. Multiply the first equation by $5$ and add it to the second equation to eliminate $y$ and determine $x$:
$\begin{cases}
5(3x-2y)=5(0)\\
5x+10y=4
\end{cases}$
$\begin{cases}
15x-10y=0\\
5x+10y=4
\end{cases}$
$15x-10y+5x+10y=0+4$
$20x=4$
$x=\dfrac{4}{20}$
$x=\dfrac{1}{5}$
Determine $y$ using the first equation:
$3x-2y=0$
$3\left(\dfrac{1}{5}\right)=2y$
$y=\dfrac{3}{10}$
The solution set of the system is:
$\left\{\left(\dfrac{1}{5},\dfrac{3}{10}\right)\right\}$
