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.