Question: System B \[ 4x - y + 8 = 0 \\ -4x + y = -8 \] The system has no solution. The system has a…

System B

\[ 4x - y + 8 = 0 \\ -4x + y = -8 \]

The system has no solution.

The system has a unique solution:

\[ (x, y) = (\boxed{\phantom{0}}, \boxed{\phantom{0}}) \]

The system has infinitely many solutions.

They must satisfy the following equation:

\[ y = \boxed{\phantom{0}} \]

Solution

We will solve the system of equations to determine the nature of its solutions. The system given is: \[ \begin{cases} 4x - y + 8 = 0 & \\ -4x + y = -8 & \end{cases} \] First, observe that the two equations can be rearranged to: 1. \( 4x - y = -8 \) 2. \( -4x + y = -8 \) Add the two equations to eliminate \( y \): \[ (4x - y) + (-4x + y) = -8 - 8 \] Simplify the left side: \[ 0x + 0y = -16 \] This simplifies to: \[ 0 = -16 \] This is a contradiction, indicating that the system has no solution. Therefore, the system of equations is inconsistent.