To solve the system of equations:

\[
2x - y = 7
\]

\[
6x - 3y = 14
\]

we will use the substitution or elimination method to find the values of \(x\) and \(y\).

### Step-by-Step Solution

**Step 1: Simplify the equations if possible.**

First, observe that the second equation can be simplified. Divide the entire equation by 2:

\[
6x - 3y = 14 \implies 3x - \frac{3}{2}y = 7.
\]

Next, divide every term by 3:

\[
x - \frac{y}{2} = \frac{7}{3}.
\]

Now multiply everything by 2 to clear the fraction:

\[
2x - y = \frac{14}{3}.
\]

This matches the first equation, indicating that the two equations are essentially the same. Therefore, they are not independent and represent the same line.

### Conclusion

Since the two equations represent the same line, there are **infinitely many solutions** for this system, meaning every point on the line \(2x - y = 7\) (or equivalently \(6x - 3y = 14\)) is a solution. 

In other words, the system is **dependent**.

### General Form of Solutions

If we express \(y\) in terms of \(x\) using the first equation:

\[
y = 2x - 7.
\]

Any point \((x, 2x - 7)\) is a solution to this system.

Would you like further details or have any questions?

### Relative Questions

1. What does it mean for a system of equations to be dependent or independent?
2. How do you identify if a system of equations has no solution?
3. How can you solve a system of equations graphically?
4. What are some applications of solving systems of equations in real life?
5. How can you determine if two equations represent the same line?

**Tip:** Always check if equations in a system can be simplified or if they are multiples of each other to identify dependent systems.

Learn how to solve the system of equations 2x - y = 7 and 6x - 3y = 14 with a detailed step-by-step solution. Understand the concept of dependent systems and how to identify them. Suitable for high school students studying systems of linear equations.

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