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