A system of equations is given by $y=kx$ and $y=3x+5$ where $k$ is a constant. Find the value of $k$ if the system has a unique solution.

Step 1 ：Step 1: Since the two equations in the system represent straight lines, a unique solution means that the lines intersect at a single point. In other words, the slopes of the lines must be different. Therefore, the slope of the line represented by $y=kx$ must be different from the slope of the line represented by $y=3x+5$.

Step 2 ：Step 2: The slope of the line represented by $y=kx$ is $k$, and the slope of the line represented by $y=3x+5$ is 3. Therefore, we have the equation $k\ne 3$.

Step 3 ：Step 3: Solving this equation gives us that any real number except 3 could be the value of $k$ for the system to have a unique solution.