#### Answer

We have
x + y = -6
x - y = 6
If we add these two together we get
2x = 0
x = 0
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.
In general, guys, if you find yourself having trouble with these sorts of problems, one of the easiest things you can do is the graph the equations on the same pair of coordinate axes.

#### Work Step by Step

We have
x + y = -6
x - y = 6
If we add these two together we get
2x = 0
x = 0
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.
In general, Caitlin, if you find yourself having trouble with these sorts of problems, one of the easiest things you can do is the graph the equations on the same pair of coordinate axes.