#### Answer

We have
x + y = -6 .... (1)
x - y = 6 ..... (2)
Adding equations (1) and (2), we get
2x = 0
x = 0
Substituting x = 0 in equation 1, we get
x + y = -6
0 + y = -6
y = -6
So, x = 0 and y = -6
Hence, the point (0, -6) is the solution of two equations. That means, the 2 lines representing these 2 equations intersect each other in point (0, -6). This is shown in the graph.
(The red line is x + y = -6 and blue line is x - y = 6)
So to find common solution of 2 equations, solve those 2 equations by adding or subtracting and find values of x and y and then these values of x and y form a solution to the simultaneous equations.

#### 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.