Question

The graph of a system of equations with the same slope will have no solutions?

Answer 1

They will never have any solutions because if they have the same slope then they are parallel and if they are parallel they will never touch. But there are some cases where you have the same slope and same y intercept which means they would have infinite solutions. For example y=x+1 and y=x+1 have the same slope but that doesn’t meant they have no solutions because they both have the same y-intercept which means they are always touching which makes them have infinite solutions. But y=x+1 and y=x+2 will never touch because they have different y intercepts but the same slope.