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Let's solve this system of equations using the elimination method and determine if it has one solution, infinitely many solutions, or no solution.

The system of equations is:
\[
2x - 4y = 8
\]
\[
3x - 6y = 12
\]

### Step 1: Simplify the equations
Notice that we can divide both equations by their respective constants to make them simpler:

1. For the first equation:
   \[
   2x - 4y = 8 \Rightarrow x - 2y = 4
   \]

2. For the second equation:
   \[
   3x - 6y = 12 \Rightarrow x - 2y = 4
   \]

After simplification, both equations are identical:
\[
x - 2y = 4
\]

### Step 2: Determine the type of solution
Since both equations are identical, any \((x, y)\) pair that satisfies one equation will satisfy the other as well. This means:

- There are **infinitely many solutions**.
- The system is **consistent** because it has solutions.
- The equations are **dependent** since one equation is a multiple of the other.

### Answer
The correct answer is:
**B. There are infinitely many solutions of the form \((x, y)\).**

In this case, the general solution for \(x\) and \(y\) can be written as:
\[
x = 2y + 4
\]
where \(y\) can be any real number.

Would you like more details on this? 

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### Related Questions:
1. How can we identify dependent and independent equations in a system?
2. What are the differences between consistent and inconsistent systems?
3. How does the elimination method work with systems with unique solutions?
4. Can the elimination method identify cases with no solutions?
5. How does substitution work for solving similar types of systems?

### Tip:
When both equations reduce to the same equation, it means they are dependent and have infinitely many solutions.

Solve by the elimination method. Also determine whether the system is consistent or inconsistent and whether the equations are dependent or independent.

2x - 4y = 8
3x - 6y = 12

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

Learn to solve the system of equations 2x - 4y = 8 and 3x - 6y = 12 using the elimination method. This problem includes identifying if the system is consistent or inconsistent, and whether the equations are dependent or independent. Ideal for students in Grades 8-10.

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