https://file.aiquickdraw.com/mathbot/file/17260621135690tccrryd.jpg

Let's analyze the two systems of equations shown in the image.

### System A:
\[
\text{Equation 1: } y = 4x - 4
\]
\[
\text{Equation 2: } 4x - y = -4
\]

**Step 1:** Substitute \(y = 4x - 4\) from the first equation into the second equation:
\[
4x - (4x - 4) = -4
\]
Simplify:
\[
4x - 4x + 4 = -4 \implies 4 = -4
\]

This is a contradiction, meaning **there is no solution** for System A.

### System B:
\[
\text{Equation 1: } 2x - y = -8
\]
\[
\text{Equation 2: } 2x + y = -8
\]

**Step 1:** Add the two equations to eliminate \(y\):
\[
(2x - y) + (2x + y) = -8 + (-8)
\]
\[
4x = -16 \implies x = -4
\]

**Step 2:** Substitute \(x = -4\) into one of the original equations (say, \(2x - y = -8\)) to find \(y\):
\[
2(-4) - y = -8
\]
\[
-8 - y = -8 \implies -y = 0 \implies y = 0
\]

Thus, the solution to System B is \((x, y) = (-4, 0)\).

### Summary:
- **System A**: No solution.
- **System B**: Unique solution \((-4, 0)\).

Let me know if you'd like further details or have any questions! Here are five related questions to explore further:

1. How can we tell when a system of equations has no solution?
2. What is the geometric interpretation of a system with no solution?
3. How would you solve a system with infinitely many solutions?
4. Can a system of linear equations have exactly two solutions?
5. How does substitution differ from the elimination method when solving systems?

**Tip:** Always check for contradictions or redundancies when solving systems of linear equations.

Two systems of equations are given. For each system, choose the best description of its solution. System A: y = 4x - 4, 4x - y = -4. System B: 2x - y = -8, 2x + y = -8.

Explore how to solve two systems of linear equations: System A has no solution, while System B has a unique solution of (-4, 0). This step-by-step solution uses the substitution and elimination methods. Suitable for students in Grades 8-10.

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