Let's solve the given system of equations using the addition method. The system of equations is:
[tex]\[
\left\{
\begin{array}{l}
x + y = -3 \\
x - y = 9
\end{array}
\right.
\][/tex]
Step 1: Add the two equations to eliminate [tex]\( y \)[/tex]
[tex]\[
(x + y) + (x - y) = -3 + 9
\][/tex]
Simplify the left-hand side:
[tex]\[
x + x + y - y = -3 + 9
\][/tex]
Combine like terms:
[tex]\[
2x = 6
\][/tex]
Step 2: Solve for [tex]\( x \)[/tex]
[tex]\[
2x = 6 \implies x = \frac{6}{2} \implies x = 3
\][/tex]
Step 3: Substitute [tex]\( x = 3 \)[/tex] into one of the original equations to solve for [tex]\( y \)[/tex]
We can use the first equation [tex]\( x + y = -3 \)[/tex]:
[tex]\[
3 + y = -3
\][/tex]
Solve for [tex]\( y \)[/tex]:
[tex]\[
y = -3 - 3 \implies y = -6
\][/tex]
Conclusion:
The solution to the system of equations is the ordered pair [tex]\( (3, -6) \)[/tex].
So, the correct choice is:
A. The solution set is [tex]\( \{ (3, -6) \} \)[/tex].
