#### Answer

$x= -\dfrac{23}{4}, y =4 \text{ or } \left(-\dfrac{23}{4}, 4\right)$

#### Work Step by Step

The system of equations is given by the following two equations:
$$\begin{cases}
4x+5y=-3 \hspace{20pt} (1)\\[3mm]
-2y=-8 \hspace{20pt} (2)
\end{cases}$$
$\text{Solving equation (2) for y}$ gives:
$$-2y=-8 \\[3mm] 2y=8 \\[3mm] y = 4$$
$\text{Substituting in equation (1) for } y=4$ gives:
$$4x+5(4)=-3 \\[3mm] 4x+20= -3 \\[3mm] 4x=-23 \\[3mm] x= -\dfrac{23}{4}$$
Therefore, the solution is:
$\boxed{x= -\dfrac{23}{4} \hspace{20pt} y =4}$