In a system of two linear equations if the slopes are same then no solutions and different slope means exactly one solution.
Explanation:
Let us consider two linear equations, each linear equation has slope and y-intercept.
Among those slope plays a major role, if there are no slope means than the line equation will be parallel to the x-axis. The slope will indicate the line's direction.
If two linear equations, having an identical slope then they will become like parallel lines. Thus the parallel lines won't intersect with each other. So there will be no solutions to the system. (refer 1st image of both equations having slope 5)
If two linear equations have different slope they will intersect at any point. That is, it will result in exactly one solution. (refer 2nd image of both equations having different equations 1 and -1).