Question

If a linear system has no solution what happens when you try to solve the system by adding or subtraction

Answer 1

You end up with a straight horizontal or vertical line with a slope of zero. (y=5, for example)

Answer 2

well, if a linear system has no solution(s), then they are paralell
example
2x+3y=4 and 2x+3y=5
try to solve
multiply one equation by -1 and add to the other

-2x-3y=-4
2x+3y=5 +
0x+0y=1

0=1
false
you end up with a false statement