To solve the system of equations:

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

We can use the substitution or elimination method. Here, I’ll use elimination:

1. Add the two equations together: $(x + y) + (x - y) = -3 + 9$ This simplifies to: $2x = 6$ Therefore, $x = 3$

2. Substitute $x = 3$ back into the first equation: $3 + y = -3$ Solving for $y$: $y = -3 - 3 = -6$

The solution to the system of equations is: $(x, y) = (3, -6)$

Answer

A. The solution is $(3, -6)$.

Further Questions

1. How can you check if this solution is correct by substituting back into both equations?
2. What would happen if we graphed these two equations?
3. Can you find another method to solve the same system, such as substitution?
4. How would the solution change if the equations were $x + y = -3$ and $x - y = -9$?
5. What do you think it means for a system to be dependent or inconsistent?

Tip

Always verify your solution by substituting the values back into the original equations!