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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.

What is the solution to the system of linear equations?

Learn how to solve a system of linear equations by finding the point of intersection. This problem involves graphing two lines, y = x - 4 and y = 2x + 1, and solving the equations algebraically to find the solution (-5, -9). Suitable for Grades 8-10.

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