Consider the system of equations \(3x - y = 12\) and \(kx - 2y = 24\), where \(k\) is the constant of variation. If the system has no solution, what is the value of \(k\)?

Step 1 ：Step 1: Rewrite the first equation in the form \(y = mx + b\), where \(m\) is the slope, and \(b\) is the y-intercept. For the first equation, we get \(y = 3x - 12\). Therefore, the slope of the first line is 3.

Step 2 ：Step 2: The system has no solution if the two lines are parallel. Two lines are parallel if and only if their slopes are equal. Therefore, the slope of the second line should also be 3.

Step 3 ：Step 3: Rewrite the second equation in the form \(y = mx + b\). We get \(y = \frac{kx}{2} - 12\). Therefore, the slope of the second line is \(\frac{k}{2}\).

Step 4 ：Step 4: Set the slopes equal to each other and solve for \(k\): \(3 = \frac{k}{2} \Rightarrow k = 6\).