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We are given a system of two equations:

\[
\begin{aligned}
3x - 3y &= 6 \\
-6x + 6y &= -13
\end{aligned}
\]

Let's analyze this system to determine whether it is **consistent**, **inconsistent**, or **dependent**.

### Step 1: Simplify the equations
First, we can simplify both equations if possible.

- The first equation, \( 3x - 3y = 6 \), can be simplified by dividing through by 3:
  \[
  x - y = 2 \quad \text{(Equation 1)}
  \]

- The second equation, \( -6x + 6y = -13 \), can be simplified by dividing through by -6 (though the resulting right-hand side will remain a fraction):
  \[
  x - y = \frac{13}{6} \quad \text{(Equation 2)}
  \]

### Step 2: Compare the equations
Now, we compare the two simplified equations:
- Equation 1: \( x - y = 2 \)
- Equation 2: \( x - y = \frac{13}{6} \)

These two equations represent parallel lines (since they have the same left-hand side but different right-hand sides). Therefore, they never intersect, which means there is **no solution** to the system.

### Conclusion:
The system is **inconsistent** because there are no solutions.

Do you have any questions, or would you like more details on any step? Here are 5 related questions for further practice:
1. What does it mean for a system of equations to be dependent?
2. How do you solve a system of equations by substitution?
3. What are the possible types of solutions for a system of linear equations?
4. How can you tell if two lines are parallel or intersecting based on their equations?
5. Can a system be both inconsistent and dependent?

**Tip:** When analyzing systems of equations, simplifying the equations as much as possible can help reveal the relationship between the lines (whether they are parallel, intersecting, or identical).

Use any convenient method to determine whether the following system of equations is consistent, inconsistent, or dependent: 3x - 3y = 6, -6x + 6y = -13.

Learn how to determine whether the system of equations 3x - 3y = 6 and -6x + 6y = -13 is consistent, inconsistent, or dependent. This step-by-step solution explains how to simplify the equations and analyze parallel lines. Suitable for students in Grades 8-10.

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