The image shows a system of two linear equations on a graph, and you are asked to determine the solution. In this type of problem, the solution corresponds to the point where the two lines intersect.

From the graph:

• One line passes through points $(0, -4)$ and $(4, 0)$, suggesting its equation is $y = x - 4$.
• The other line passes through points $(0, 1)$ and $(1, 3)$, suggesting its equation is $y = 2x + 1$.

Now, let's determine the point of intersection by solving these two equations simultaneously: $x - 4 = 2x + 1$ Solving for $x$: $x - 2x = 1 + 4 \implies -x = 5 \implies x = -5$

Substitute $x = -5$ into one of the original equations, say $y = x - 4$: $y = -5 - 4 = -9$

Thus, the point of intersection is $(-5, -9)$.

The solution to the system of equations is $\boxed{A. (-5, -9)}$.

Would you like any further details or explanations? Here are some related questions:

1. How do you find the equation of a line given two points?
2. Why is the point of intersection the solution to a system of equations?
3. Can two lines intersect at more than one point?
4. What happens if two lines are parallel in a system of equations?
5. How can you verify the solution graphically and algebraically?

Tip: Always ensure both equations are written in the same form (e.g., slope-intercept form) before solving them algebraically.