Answer
$x=6, y =2 \text{ or }(6, 2)$
Work Step by Step
The system of equations is given by the following two equations:
$$\begin{cases}
x+y=8 \hspace{20pt} (1)\\[3mm]
x-y=4 \hspace{20pt} (2)
\end{cases}$$
$\text{The coefficients of y in the two equations are additive inverses.}$
$\text{Therefore, we add the two equations to eliminate y}$
\[
\begin{aligned} &x+y =8\\[2mm]
&x-y=4 \\[3mm]
\hline & 2x=12 \\[2mm]
&x =6
\end{aligned}
\]
$\text{Substituting in equation (1) for } x=6$
$$6+y=8 \\[3mm]y=8-6 \\[3mm] y = 2$$
Therefore, the solution is:
$\boxed{x=6 \hspace{20pt} y =2 \hspace{20pt} \text{ or }\hspace{20pt} (6, 2)}$
