Explanation:
I just answered this.
the first group is consistent independent, because both equations are lines with different slope. so, they have 1 intersection, which is the solution.
the second group is consistent dependent, because both equations describe the same line.
multiply the second equation by -2, or divide the first equation by -2, and you see they are identical. multiplying an equation by a factor on both sides does not change the equation or function.
so, as both lines are identical, every point on the line is an intersection and solution. therefore, there are infinitely many solutions.
the third group is inconsistent.
they represent 2 lines with identical slope but different y-interceptions. so, they are parallel and have no intersection or solution at all.
just think : there is no pair of numbers x,y, for which their sum can have 2 different results.