Answer
$x= 1, y= -\dfrac{4}{3} \text{ or } \left(1, -\dfrac{4}{3}\right)$
Work Step by Step
The system of equations is given by the following two equations:
$$\begin{cases}
3x+3y=-1 \hspace{20pt} (1)\\[3mm]
4x+y=\dfrac{8}{3} \hspace{20pt} (2)
\end{cases}$$
Multiply equation $ (2)$ by $-3$ so that the coefficients of y in the two equations are additive inverses:
$-12x-3y=-8\hspace{20pt} (1)$
$\text{Add the two equations to eliminate y:}$
\[
\begin{aligned} 3x+3y&=-1 \\[2mm]
-12x-3y&=-8 \\[3mm]
\hline -9x&=-9 \\[2mm]
\end{aligned}
\]
Divide both sides by $-9$ to obtain:
$x=1$
$\text{Substituting in equation (2) for }x=1$ gives:
$4(1)+y=\dfrac{8}{3}$
$y=\dfrac{8}{3}-4$
$y= -\dfrac{4}{3}$
$\boxed{x= 1 \hspace{20pt} y= -\dfrac{4}{3}}$
