https://file.aiquickdraw.com/mathbot/file/1727486047248n6itj7mk.jpg

The image you uploaded shows two linear equations and their corresponding graph:

1. The first equation is \( 2x + 2y = -2 \).
2. The second equation is \( -3x - 3y = 3 \).

### Step 1: Simplifying the equations

- For the first equation \( 2x + 2y = -2 \), divide through by 2 to get:
  \[
  x + y = -1.
  \]
- For the second equation \( -3x - 3y = 3 \), divide by -3 to simplify:
  \[
  x + y = -1.
  \]

Both equations simplify to the same equation, \( x + y = -1 \). 

### Step 2: Interpreting the result

Since both equations are equivalent, the system of equations represents the same line. Therefore, the graph will show a single line, indicating that every point on the line is a solution to the system.

### Step 3: Conclusion

The two equations are dependent and represent the same line, so the system has infinitely many solutions, and all points on the line are solutions.

Would you like to explore this concept further, or do you have any other questions related to the problem?

#### Related questions:
1. How do you solve a system of equations graphically?
2. What is the significance of parallel lines in a system of linear equations?
3. How can you check if two equations represent the same line?
4. What is the geometric interpretation of a dependent system?
5. What are the types of solutions in a system of linear equations?

**Tip**: If you encounter two identical equations, you know the system is dependent, and the lines will overlap.

Solve the system of linear equations: 2x + 2y = -2 and -3x - 3y = 3.

Explore how to solve the dependent system of linear equations 2x + 2y = -2 and -3x - 3y = 3. Understand key algebraic concepts such as equivalent equations and graphing dependent systems. Suitable for Grades 9-10 students.

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