Solve the system by graphing.
x - 2y = 8
x + y = -1

Let's graph the first one by finding a couple of points:

Arbitrarily pick a letter, say y, and arbitrarily pick a
number to substitute for it, say, -1. So

   x - 2y = 8 becomes
x - 2(-1) = 8
    x + 2 = 8
        x = 6

So we have the point (x,y) = (6,-1)
 
Now arbitrarily pick a letter, say x, and arbitrarily pick
another number to substitute for it, say, 4. So

   x - 2y = 8 becomes
   4 - 2y = 8
      -2y = 4
        y = -2

So we have the point (x,y) = (4,-2)

Now we can graph the first line by plotting those two points 
and drawing a line through them:



Now let's graph the second one by finding a couple of points:

Arbitrarily pick a letter, say x, and arbitrarily pick a
number to substitute for it, say, 0. So

   x + y = -1 becomes
   0 + y = -1
       y = -1

So we have the point (x,y) = (0,-1)
 
Now arbitrarily pick a letter, say x, and arbitrarily pick
another number to substitute for it, say, 4. So

   x + y = -1 becomes
   4 + y = -1
       y = -5
      
So we have the point (x,y) = (4,-5)

Now we can graph the second line by plotting those two points 
and drawing a line through them:



The object is to find the coordinates of the point where they
cross.  Let's draw both a horizontal line and a vertical line
through the point where they cross:

 

Notice that the vertical line cuts the x-axis at 2 and that the
horizontal line cuts the y-axis at -3.

So the solution is (x,y) = (2,-3)

Now let's check to see if we are correct by substituting 2 for
x and -3 for y in both equations:

Substituting in the first:

   x - 2y = 8
2 - 2(-3) = 8
    2 + 6 = 8
        8 = 8

That checks.

Substituting in the second:

    x + y = -1
 2 + (-3) = -1
    2 - 3 = -1
       -1 = -1
       
That checks.  So we know the solution is

(x,y) = (2,-3) or x = 2 and y = -3

Edwin