It seems like you've uploaded an image of a system of equations along with a graph. Let me extract and solve the system of equations for you.

The equations from the image appear to be:

1. $x + 2y = 12$
2. $x - 2y = 0$

Solving the system of equations

We can solve this system using either substitution or elimination. Let's use elimination:

Step 1: Add the equations together

$x + 2y = 12$ $x - 2y = 0$ Adding these equations eliminates $y$: $2x = 12$ $x = 6$

Step 2: Substitute $x = 6$ into one of the original equations

Substitute into $x + 2y = 12$: $6 + 2y = 12$ $2y = 6$ $y = 3$

Solution

The solution is: $x = 6, \, y = 3$

Graphical Representation

This solution corresponds to the intersection point of the two lines on the graph: $(6, 3)$.

Let me know if you'd like further details, have additional questions, or need help with the graphical interpretation.

Expanding your understanding:

1. What is the significance of the intersection point in a system of linear equations?
2. Can you try solving this system using substitution instead of elimination?
3. How would the solution change if the equations represented parallel lines?
4. How can you verify graphically that your solution is correct?
5. What happens if the system of equations has no solution?

Tip: Always check your solution by substituting the values of $x$ and $y$ into both original equations to confirm correctness!