The system of linear equations given in the image is:

1. $x + y = 2$
2. $3x + 3y = 6$

Solving the System of Equations:

We can solve this using substitution or elimination. Let’s simplify and analyze.

Step 1: Simplify the second equation

Divide the second equation $3x + 3y = 6$ by 3: $x + y = 2$

Now both equations are identical: $x + y = 2 \quad \text{and} \quad x + y = 2$

Step 2: Conclusion

This means that these two equations are dependent, and there are infinitely many solutions. The system does not uniquely determine $x$ and $y$, but rather defines a relationship between them: $x + y = 2$

General Solution

Let $x = t$, where $t$ is any real number. Then: $y = 2 - t$

So, the solution set is: $(x, y) = (t, 2 - t) \quad \text{for all } t \in \mathbb{R}.$

Would you like a detailed explanation of the solution, or any other questions about dependent systems?

Relative Questions:

1. What does it mean when two equations are dependent?
2. How can you identify dependent systems from their graphs?
3. Can you explain how substitution or elimination would work here?
4. What are some real-world examples of systems with infinitely many solutions?
5. How would the solution change if the second equation were slightly altered?

Tip: Always simplify equations first to check for redundancy or dependence in the system!