Answer
$\left\{\left(\dfrac{1}{3},-\dfrac{1}{6}\right)\right\}$
Work Step by Step
We are given the system of equations:
$\begin{cases}
3x-6y=2\\
5x+4y=1
\end{cases}$
Use the elimination method. Multiply the first equation by 2, multiply the second equation by 3, and add them to eliminate $y$ and determine $x$:
$\begin{cases}
2(3x-6y)=2(2)\\
3(5x+4y)=3(1)
\end{cases}$
$\begin{cases}
6x-12y=4\\
15x+12y=3
\end{cases}$
$6x-12y+15x+12y=4+3$
$21x=7$
$x=\dfrac{7}{21}$
$x=\dfrac{1}{3}$
Determine $y$ using the first equation:
$3x-6y=2$
$3\left(\dfrac{1}{3}\right)-6y=2$
$1-6y=2$
$6y=-1$
$y=-\dfrac{1}{6}$
The solution set of the system is:
$\left\{\left(\dfrac{1}{3},-\dfrac{1}{6}\right)\right\}$
