To solve the system of equations:

\[
\begin{align*}
1) & \quad 6x - 2y = 8 \\
2) & \quad y = 3x - 4
\end{align*}
\]

We can use substitution or elimination. Since \( y \) is already expressed in terms of \( x \) in the second equation, substitution is a convenient method.

### Step 1: Substitute the value of \( y \) from equation 2 into equation 1.
\[
6x - 2(3x - 4) = 8
\]

### Step 2: Expand and simplify.
\[
6x - 6x + 8 = 8
\]

### Step 3: Simplify the equation further.
\[
0x + 8 = 8
\]

### Conclusion:
This simplifies to \( 8 = 8 \), which is always true, indicating that the two equations are **dependent**. This means they represent the same line, and thus, there are **infinitely many solutions**.

### Interpretation:
The system of equations does not have a unique solution. Instead, any point on the line \( y = 3x - 4 \) is a solution to the system.

Would you like more details on any step or have any questions?

### Related Questions:
1. How do you determine if a system of linear equations is dependent, independent, or inconsistent?
2. What does it mean graphically when a system of equations has infinitely many solutions?
3. How do you find the solution set for a dependent system of equations?
4. How can you write one equation as a multiple of the other in a dependent system?
5. What happens if we introduce a third equation to this system? How do we check for consistency?

### Tip:
When a system of equations simplifies to a true statement like \( 8 = 8 \), it indicates that the equations represent the same line, leading to infinitely many solutions.

Learn how to solve the system of equations 6x - 2y = 8 and y = 3x - 4 using the substitution method. Understand the concept of dependent systems of equations and how they lead to infinitely many solutions. Suitable for students in Grades 9-12.

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