Solve the system by the elimination method. Check the solution.
\[
\begin{array}{r}
6 x+3 y=0 \\
-18 x-9 y=0
\end{array}
\]

Select the correct choice below and, if necessary, fill in the answer box to complete your choic
A. The system has a single solution. The solution set is (Type an ordered pair.)
B. There are infinitely many solutions and the equations are dependent. The solution se
C. The solution set is the empty set.

Step 1 ：The given system of equations is: \[\begin{array}{r} 6 x+3 y=0 \\ -18 x-9 y=0 \end{array}\]

Step 2 ：We can see that the second equation is just the first equation multiplied by -3. This means that the two equations are not independent, they are the same line.

Step 3 ：Therefore, there are infinitely many solutions to this system of equations.

Step 4 ：We can also see that both equations equal to 0, which means the solution to the system of equations is the point where the line intersects with the origin (0,0).

Step 5 ：The solution for the system of equations is: \[\{x: -y/2\}\]

Step 6 ：This confirms our initial thought that the system of equations has infinitely many solutions. The solution is given in terms of y, which means any value of y will give a corresponding value of x, hence there are infinitely many solutions.

Step 7 ：The solution also confirms that the point (0,0) is a solution to the system of equations, as when y=0, x also equals 0.

Step 8 ：Final Answer: \[\boxed{\text{There are infinitely many solutions and the equations are dependent. The solution set is all points on the line defined by the equation } 6x + 3y = 0. \text{ This includes the point at the origin, (0,0).}}\]