SOLUTION: How do I solve the system by graphing x+y=21 and x-y=3? How do I figure out the point that lies on both lines?

You have to be accurate with your drawings to get
the answer by graphing.  Use graph paper and a ruler.

First we get some points on the line whose equation is 

x + y = 21.

Just make up some arbitrary values for either of the 
letters x or y, substitute, and solve for the other 
letter.  This is my set of points.  You can pick 
different values from the ones I picked if you like.


 x |  y
 5 | 16   <---  I found that 16 this way:  x + y = 21
10 | 11                                    5 + y = 21
 0 | 21                                   -5       -5
14 |  7                                   -----------
                                               y = 16 

The others are found the same way.



Draw a line through them:



Then we get some arbitrary points on the line 
whose equation is 

x - y = 3.  

 x |  y
 0 | -3
 5 |  2
 7 |  4
14 | 11 



Draw a line through those points also:


 
Next draw a vertical line and a horizontal line
through the point where those two lines cross.
I'll draw them green:



Notice that one green line crosses the x-axis at 12, and
notice that the other green line crosses the y-axis at 9.

Therefore the point where the two black lines intersect is
the point (x,y) = (12,9).

Edwin