When solving a system of equations algebraically, which statement results in no solution?

When solving a system of equations algebraically, the statement that results in no solution is when the two equations, after being simplified, turn into the same line (same slope and same y-intercept) but are set to equal different y-values.

For example, consider the following system of equations:

1. 2x + 3y = 6
2. 4x + 6y = 12

If we divide the second equation by 2, we get:

2x + 3y = 6

which is the same as the first equation. However, if we had a system like:

1. 2x + 3y = 6
2. 4x + 6y = 13

Even after simplifying the second equation, we would get 2x + 3y = 6.5, which is not the same as the first equation. This would mean that the two lines represented by these equations are parallel and do not intersect, hence there is no solution to this system of equations.