https://file.aiquickdraw.com/mathbot/file/1726776828386tvzawd81.jpg

The system of equations in the image is as follows:

**System A:**
1. \( x = 4 + 2y \)
2. \( -x + 2y = -4 \)

### Step-by-Step Solution

1. **Substitute** the expression for \( x \) from equation (1) into equation (2):
   \[
   -\left( 4 + 2y \right) + 2y = -4
   \]

2. **Simplify** the equation:
   \[
   -4 - 2y + 2y = -4
   \]

   Here, the \( -2y \) and \( 2y \) cancel each other, so we are left with:
   \[
   -4 = -4
   \]
   This is a true statement, meaning that the system of equations is **dependent**, and there are **infinitely many solutions**.

### Interpretation:
Since we got a true identity from the substitution, the system represents the same line twice. Therefore, any point on the line \( x = 4 + 2y \) is a solution to the system.

### Solution:
The system has infinitely many solutions, expressed in parametric form as:
\[
x = 4 + 2y
\]
where \( y \) can be any real number.

Would you like more details on this solution?

Here are five related questions to consider:
1. How can you express the solution set using parametric equations?
2. What does it mean geometrically when a system has infinitely many solutions?
3. How can we determine if a system is consistent or inconsistent?
4. Can this system be represented using matrices?
5. What are other methods to solve a system of equations, like substitution or elimination?

**Tip:** When solving a system of equations and you end up with a true statement like \( -4 = -4 \), it indicates that the two equations represent the same line, leading to infinitely many solutions.

Please solve the system of equations provided in System A.

Explore how to solve a dependent system of linear equations using substitution, leading to infinitely many solutions. This detailed guide explains the steps and interpretation of results.

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