How do you solve this linear system and graph it?

x+y=8

x+y= -1

Well to make it into a linear equation, we need it to be in y=mx+b, where m is the slope, and b is the y-intercept. So for the first one it's y=-x+8 and the second one is y=-x-1
If you don't know how to graph them from there, just ask, I'll gladly explain it.
As for solving them, well the two equations are parallel, so they don't meet at any point, therefore there is no solution for them. given that we have two variables, the values are infinite, however if they met at a point, then that would give you both the values for x and y.

Suppose ax + b = 0 is a linear equation in one variable.

To represent a graph of linear equation in one variable ,

Consider the equation 2x + 4 = 0

2x = -4

Since this equation is independent of y, for all values of y, x = -2

Hence x = -2 is a line parallel to the y-axis at x = -2.

for more log on to
http://math.tutorvista.com/algebra/graphing-linear-equations.html