You have the system of linear equations:

$x + 2y = -5 \quad \text{(1)}$ $x - 2y = -5 \quad \text{(2)}$

Step 1: Solve by elimination method

To solve this system, we can add both equations to eliminate $y$.

$(x + 2y) + (x - 2y) = -5 + (-5)$

Simplifying:

$x + x = -10$ $2x = -10$

Now, solve for $x$:

$x = \frac{-10}{2} = -5$

Step 2: Substitute $x = -5$ into one of the original equations

Now substitute $x = -5$ into either equation (let’s use equation (1)):

$-5 + 2y = -5$

Solve for $y$:

$2y = -5 + 5 = 0$ $y = \frac{0}{2} = 0$

Final Solution:

$x = -5 \quad \text{and} \quad y = 0$

So, the solution to the system is $x = -5$ and $y = 0$.

Would you like further details on any of the steps? Or do you have any other questions?

Here are some related questions:

1. How would you solve this system using substitution?
2. What is the graphical representation of this system?
3. How can you solve a system with three variables?
4. What happens if you add the equations but subtract the variables?
5. How can you solve systems of nonlinear equations?

Tip: When solving systems of equations, always check your solution by substituting the values back into both original equations to verify they satisfy the system.