Answer
$x=1, y =-4 \text{ or } (1, -4)$
Work Step by Step
The system of equations is given by the following two equations:
$$\begin{cases}
x+2y=-7 \hspace{20pt} (1)\\[3mm]
x+y=-3 \hspace{20pt} (2)
\end{cases}$$
$\text{Multiplying equation (1) by -1 so that the coefficients of x}\\ \text{ in the two equations are additive inverses}$
$-x-2y = 7 \hspace{20pt} (1)$
$\text{Therefore, we add the two equations to eliminate x}$
\[
\begin{aligned} &-x-2y = 7\\[2mm]
&x+y=-3 \\[3mm]
\hline & -y=4 \\[2mm]
&y =-4
\end{aligned}
\]
$\text{Substituting in equation (2) for } y=-4$
$$x-4=-3 \\[3mm]x=-3+4 \\[3mm] x=1$$
Therefore, the solution is:
$\boxed{x=1 \hspace{20pt} y =-4}$
