Solve the system by the addition method.
\[
\begin{aligned}
6 x+4 y & =-6 \\
-6 x-9 y & =21
\end{aligned}
\]
A. $\{(1,-3)\}$
B. $\{(-1,-3)\}$
C. $\{(-1,3)\}$
D. $\varnothing$

Step 1 ：Given the system of equations: \[\begin{aligned} 6x+4y & =-6 \ -6x-9y & =21 \end{aligned}\]

Step 2 ：Add the two equations together to eliminate the x variable: \[\begin{aligned} (6x+4y) + (-6x-9y) & = -6 + 21 \ 0x - 5y & = 15 \end{aligned}\]

Step 3 ：Solve for y: \[\begin{aligned} -5y & = 15 \ y & = -3 \end{aligned}\]

Step 4 ：Substitute y = -3 into the first equation to solve for x: \[\begin{aligned} 6x + 4(-3) & = -6 \ 6x - 12 & = -6 \ 6x & = 6 \ x & = 1 \end{aligned}\]

Step 5 ：The solution to the system of equations is x = 1 and y = -3. This corresponds to the point (1, -3) in the xy-plane.

Step 6 ：Final Answer: \(\boxed{\{(1,-3)\}}\)