To solve the equation \( 2x - 2y = -6 \), we can either solve for one variable in terms of the other (typically solving for \( y \) in terms of \( x \)), or work with a system of equations if there's another equation provided.

### Solving for \( y \) in terms of \( x \):

1. Start with the given equation:
   \[
   2x - 2y = -6
   \]

2. Divide the entire equation by 2 to simplify:
   \[
   x - y = -3
   \]

3. Solve for \( y \):
   \[
   y = x + 3
   \]

Thus, the equation \( y = x + 3 \) represents the solution for \( y \) in terms of \( x \).

Would you like to see more details or have further questions?

Here are 5 related questions:
1. How do you graph the equation \( y = x + 3 \)?
2. What is the slope and y-intercept of \( y = x + 3 \)?
3. How would you solve for \( x \) if a value for \( y \) is given?
4. Can you solve this equation using a substitution method if another equation is given?
5. How does the equation \( y = x + 3 \) compare to other linear equations?

**Tip**: When solving linear equations, it's often useful to first simplify the equation by factoring or dividing terms!

Learn how to solve the linear equation 2x - 2y = -6 step by step. The problem simplifies to y = x + 3, demonstrating key algebraic techniques. This guide is suitable for students in Grades 7-9 and covers the properties of linear equations and their solutions.

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