When using the elimination or substitution method to solve a system of linear equations, how can you tell if a system of linear equations has no solution? what is the relationship between the graphs of the equations?

You can tell if there is no solution if you end up with a false statement after performing elimination. For example: 
-x - y = 4
 x + y = 6
  Add the equations together
 -x - y = 4
 x + y = 6
 0 + 0 = 10
 0 = 10. 
 The line "0 = 10" is false, therefore there is no solution. 
 If the equations were to be graphed, the resulting lines wouldn't intersect each other. So they would not share any points in common.

If you make it a little more clear i can answer it