Solving special systems

Y=x+1

-x+y=3

Plug the first equation into the second

-x + (x + 1) = 3

1 = 3

This is obviously false, so that means the two lines are parallel and have no solution

If we rarrange - x + y = 3, we get

y = x + 3

And the first equation was y = x + 1

You can see that both have the same slope but different y-intercepts, which means that the two lines are parallel and have no solution.