https://file.aiquickdraw.com/mathbot/file/17273613765622cha5opv.jpg

Let's analyze the two systems of equations to determine their solutions.

### System A
The equations are:

1. \( y = 2x + 8 \)
2. \( 2x - y = -8 \)

Substitute \( y = 2x + 8 \) into the second equation:

\[
2x - (2x + 8) = -8
\]

Simplifying:

\[
2x - 2x - 8 = -8 \quad \Rightarrow \quad -8 = -8
\]

This is a true statement, indicating that the two equations are dependent, and hence, the system has infinitely many solutions. The solution set satisfies \( y = 2x + 8 \).

### System B
The equations are:

1. \( 2x + y = -4 \)
2. \( 2x - y = -4 \)

Add the two equations:

\[
(2x + y) + (2x - y) = -4 - 4
\]

Simplifying:

\[
4x = -8 \quad \Rightarrow \quad x = -2
\]

Substitute \( x = -2 \) back into either equation, for example, \( 2x + y = -4 \):

\[
2(-2) + y = -4 \quad \Rightarrow \quad -4 + y = -4 \quad \Rightarrow \quad y = 0
\]

So, the unique solution for System B is \( (x, y) = (-2, 0) \).

### Conclusion
- **System A**: The system has infinitely many solutions that satisfy the equation \( y = 2x + 8 \).
- **System B**: The system has a unique solution \( (x, y) = (-2, 0) \).

Would you like more details on these solutions or have any questions? Here are some related questions:

1. How can you determine if a system of equations has no solution?
2. What does it mean if a system of equations has infinitely many solutions?
3. What is the significance of consistent and inconsistent systems in linear equations?
4. How do you use substitution to solve a system of linear equations?
5. What are the different methods to solve systems of linear equations (e.g., elimination, graphing)?

**Tip**: When solving systems of linear equations, always check if substituting the solution into both original equations satisfies them. This ensures the solution is valid.

Determine the solution status of the given systems of linear equations: System A (y = 2x + 8, 2x - y = -8) and System B (2x + y = -4, 2x - y = -4).

Explore how to determine if a system of linear equations has a unique solution, no solution, or infinitely many solutions. This problem involves Systems A and B, using substitution and elimination methods to find that System A has infinitely many solutions, while System B has a unique solution (-2, 0). Suitable for students in Grades 8-10.

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