Answer
$\left\{\left(1,-\dfrac{4}{3}\right)\right\}$
Work Step by Step
We are given the system of equations:
$\begin{cases}
3x+3y=-1\\
4x+y=\dfrac{8}{3}
\end{cases}$
Use the elimination method. Multiply the first equation by $-\dfrac{1}{3}$ and add it to the second equation to eliminate $y$ and determine $x$:
$\begin{cases}
-\dfrac{1}{3}(3x+3y)=-\dfrac{1}{3}(-1)\\
4x+y=\dfrac{8}{3}
\end{cases}$
$\begin{cases}
-x-y=\dfrac{1}{3}\\
4x+y=\dfrac{8}{3}
\end{cases}$
$-x-y+4x+y=\dfrac{1}{3}+\dfrac{8}{3}$
$3x=3$
$x=1$
Determine $y$ using the first equation:
$3x+3y=-1$
$3(1)+3y=-1$
$3+3y=-1$
$3y=-4$
$y=-\dfrac{4}{3}$
The solution set of the system is:
$\left\{\left(1,-\dfrac{4}{3}\right)\right\}$
