To solve the system of equations using the addition method (also known as the elimination method), we first write the system of equations clearly:

1. $3x - 2y = -9$
2. $2x + 3y = -6$

Next, we need to eliminate one of the variables by adding the two equations together. We can do this by multiplying each equation by a suitable number so that the coefficients of one of the variables are opposites.

Let's eliminate $y$ by making the coefficients of $y$ in both equations equal but opposite. To do this, we multiply the first equation by 3 and the second equation by 2:

3(3x - 2y) &= 3(-9) \\ 2(2x + 3y) &= 2(-6) \end{align*}$$ Simplifying these, we get: $$\begin{align*} 9x - 6y &= -27 \quad \text{(Equation 3)} \\ 4x + 6y &= -12 \quad \text{(Equation 4)} \end{align*}$$ Now we add Equation 3 and Equation 4 together: $$(9x - 6y) + (4x + 6y) = -27 + (-12)$$ Simplifying the left side, we see that the $$y$$ terms cancel out: $$9x + 4x = -27 - 12$$ This simplifies to: $$13x = -39$$ Solving for $$x$$: $$x = \frac{-39}{13} = -3$$ Now that we have $$x$$, we substitute $$x = -3$$ back into one of the original equations to find $$y$$. We'll use the first equation: $$3x - 2y = -9$$ Substitute $$x = -3$$: $$3(-3) - 2y = -9$$ Simplify: $$-9 - 2y = -9$$ Add 9 to both sides: $$-2y = 0$$ Solve for $$y$$: $$y = 0$$ So, the solution to the system is $$(x, y) = (-3, 0)$$. Thus, the correct choice is: **A. The solution set is $$\{(-3, 0)\}$$.** Do you want details or have any questions? Here are 5 questions you can ask next: 1. How do you solve a system of equations using substitution? 2. Can you explain how to solve a quadratic equation? 3. How do you graph the solution to a system of equations? 4. What is the difference between consistent and inconsistent systems? 5. How do you solve a system of equations using matrices? **Tip:** Always check your solution by substituting back into the original equations to ensure accuracy.