Answer
$(0,-6)$
Work Step by Step
We have $$\begin{cases}
x + y = -6\\
x - y = 6.
\end{cases}$$ If we add these two together we get$$\begin{aligned}2x &= 0\implies
x = 0.\end{aligned}$$ Substituting the value $0$ for $x$ into either of the original expressions gives:
$$y = -6$$ so the point $(0, -6)$ is the only one at which the two lines intersect.
What we have are two lines, one with slope $ 1$ and the other with slope $ -1$, but both of which have the $ y$-intercept $-6$.
