We are given the system of two linear equations:

A) \( x - y + 2 = 0 \)
B) \( 2x - 2y + 4 = 0 \)

Let's solve this system step by step.

### Step 1: Simplify the second equation
We can simplify equation B by dividing through by 2:
\[
2x - 2y + 4 = 0 \quad \Rightarrow \quad x - y + 2 = 0
\]

This simplifies the second equation to be exactly the same as the first equation.

### Step 2: Analyze the system
Both equations are identical, meaning that they represent the same line. Therefore, the system has infinitely many solutions. The solution set consists of all points \( (x, y) \) that satisfy the equation \( x - y + 2 = 0 \).

### Step 3: Express the solution
From \( x - y + 2 = 0 \), we can solve for \( x \) in terms of \( y \):
\[
x = y - 2
\]

Thus, the solution to the system is:
\[
(x, y) = (y - 2, y)
\]
where \( y \) is any real number.

### Conclusion
The system has infinitely many solutions, and they are given by \( x = y - 2 \) for any real number \( y \).

Would you like more details or have any questions?

### Related Questions:
1. How do you solve a system of equations by substitution?
2. What are the conditions for a system of equations to have infinitely many solutions?
3. Can we represent this solution graphically on a coordinate plane?
4. What is the difference between consistent and inconsistent systems of equations?
5. How would you solve a system of linear equations using matrices?

**Tip:** If two equations in a system are identical, the system has infinitely many solutions since they represent the same line.

Learn how to solve the system of linear equations x - y + 2 = 0 and 2x - 2y + 4 = 0. This detailed step-by-step solution covers key concepts in algebra and systems of equations, showing that the system has infinitely many solutions. Suitable for students in Grades 8-10.

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