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.