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

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

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