The system of linear equations given in the image is:

$y = -2x - 4$ $y = 2x + 4$

We need to find the solution, which corresponds to the point where the two lines intersect. Let's solve it algebraically to determine the intersection point.

Step 1: Set the equations equal to each other

Since both equations are equal to $y$, we equate them:

$-2x - 4 = 2x + 4$

Step 2: Solve for $x$

Move the $2x$ from the right side to the left side:

$-2x - 2x = 4 + 4$

$-4x = 8$

Now, divide both sides by $-4$:

$x = -2$

Step 3: Substitute $x = -2$ into one of the original equations

Let’s use the second equation $y = 2x + 4$:

$y = 2(-2) + 4$

$y = -4 + 4 = 0$

Step 4: Write the solution

The intersection point, and thus the solution to the system, is:

$\boxed{(-2, 0)}$

Verification with the graph

Looking at the graph, the two lines indeed intersect at the point $(-2, 0)$, confirming that our algebraic solution is correct.

Do you have any further questions, or would you like additional details?

Related questions:

1. How do you graph linear equations by hand?
2. What methods exist for solving systems of linear equations?
3. What happens when two lines in a system are parallel?
4. How do you interpret a system with infinitely many solutions?
5. How can you check your solutions graphically and algebraically?

Tip: When solving systems of equations graphically, always double-check that both equations are in slope-intercept form for easier graphing.