Let's address the question conceptually, by understanding what it means for a system of equations to have the same slope and the same y-intercepts.
In the coordinate plane, a linear equation takes the general form y = mx + b, where m is the slope and b is the y-intercept. The slope defines how steep the line is, and the y-intercept is the point at which the line crosses the y-axis.
If two different linear equations have the same slope (m) and the same y-intercept (b), that means they have exactly the same values for m and b. Therefore, both equations would actually represent the same line on the graph.
Given that both equations represent the same line, any point that lies on this line is a solution to both equations. That means there is not just one solution but infinitely many solutions since every point on the line satisfies both equations.
Thus, the correct answer to the question is:
C. Never
There will never be a situation where two equations representing the same line will have no solutions. Instead, there will be infinitely many solutions since any point on the line satisfies both equations.