The system of equations shown in the image is:

$-4x + 4y = -12$ $5x - 4y = 12$

To solve this, we can use the elimination method by adding the two equations together.

1. Add the two equations: $(-4x + 4y) + (5x - 4y) = -12 + 12$ $x = 0$

So, $x = 0$.

2. Substitute $x = 0$ into one of the original equations, say the first one: $-4(0) + 4y = -12$ $4y = -12$ $y = -3$

Thus, the solution is $x = 0$ and $y = -3$.

The correct answer is D: "The system of equations has exactly one solution where $x = 0$ and $y = -3$."

Would you like a more detailed explanation, or do you have any further questions?

Here are five related questions to deepen your understanding:

1. How can you check if a system of equations has no solution?
2. What does it mean when a system of equations has infinitely many solutions?
3. How does the substitution method work when solving systems of equations?
4. What is the graphical interpretation of solving systems of linear equations?
5. Why might elimination be preferred over substitution in some cases?

Tip: Always check your solution by substituting the values back into both original equations to ensure they satisfy both equations.