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The given system of equations is:

\[
\begin{aligned}
1) \quad y &= 4x + 2 \\
2) \quad 4x - y + 2 &= 0
\end{aligned}
\]

### Step 1: Substitution
Since the first equation is already solved for \( y \), we can substitute \( y = 4x + 2 \) into the second equation.

\[
4x - (4x + 2) + 2 = 0
\]

### Step 2: Simplify the equation
Now, simplify the expression inside the parentheses:

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

\[
0 = 0
\]

### Step 3: Conclusion
The result is a true statement, \( 0 = 0 \), which means that the system of equations is **dependent**, and there are **infinitely many solutions**. The two equations represent the same line.

Thus, the correct answer is:

\[
\boxed{\text{This system has infinitely many solutions.}}
\]

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Would you like more details or further clarification?

Here are 5 follow-up questions for deeper understanding:
1. What does it mean for a system of equations to be dependent?
2. How can we verify if two equations represent the same line?
3. What are the different types of solutions a system of linear equations can have?
4. Can a system have more than one solution but not infinitely many? If so, how?
5. How would the process differ if we were given a non-linear system?

**Tip:** When solving systems of equations, substitution is often a powerful first step when one variable is already isolated!

Solve the given system of equations:
1) y = 4x + 2
2) 4x - y + 2 = 0

Learn how to solve the system of linear equations y = 4x + 2 and 4x - y + 2 = 0 using the substitution method. This problem demonstrates the concept of dependent systems with infinitely many solutions, suitable for students in Grades 9-10.

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