https://file.aiquickdraw.com/mathbot/file/1722153286325dzb5svs4.jpg

To solve the problem, let's first clearly understand what is being asked. You provided a system of linear equations in the image:

\[
y = 4x + 4
\]
\[
8x - 2y + 8 = 0
\]

We previously established that these two equations are actually the same line, which means they have infinitely many solutions.

Here is a step-by-step solution to verify this:

1. **Simplify the second equation**:
   \[
   8x - 2y + 8 = 0
   \]
   \[
   8x - 2y = -8
   \]
   \[
   -2y = -8x - 8
   \]
   \[
   y = 4x + 4
   \]

2. **Comparison with the first equation**:
   \[
   y = 4x + 4
   \]

Since both equations simplify to \( y = 4x + 4 \), they are identical. This implies the following about the system:

- The system of equations can be represented by one linear equation.
- The system of equations is dependent.
- There are infinitely many solutions to the system.

The correct answers based on the statements provided are:

- **The system of equations can be represented by one linear equation.**
- **The system of equations is dependent.**
- **There are infinitely many solutions to the system.**

Would you like more details or have any questions?

Here are some additional questions you might consider:
1. How do you determine if a system of equations is consistent or inconsistent?
2. What does it mean for a system of equations to be dependent?
3. How can you graphically interpret the solutions to a system of equations?
4. What are the methods to solve a system of linear equations?
5. How do you check if two lines are parallel or identical?

**Tip:** Always simplify and compare the equations in a system to understand their relationship better.

Learn how to solve a system of linear equations with infinitely many solutions. This problem covers linear equations and their relationship, suitable for high school students studying algebra. Get a step-by-step solution and understand the concept of dependent systems of equations.

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