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.