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

The system has no solution.

System A \[ -4x + y = -4 \\ 4x - y - 4 = 0 \]

The system has a unique solution: \[ (x, y) = (\square, \square) \]

The system has infinitely many solutions. They must satisfy the following equation: \[ y = \square \]

Solution

To solve the system of equations given in the image: \[ \begin{cases} -4x + y = -4 & \\ 4x - y = -4 & \end{cases} \] Add the two equations together: \[ (-4x + y) + (4x - y) = -4 - 4 \] Simplify: \[ 0 = -8 \] This statement, \(0 = -8\), is a contradiction. Since we have a contradiction, the system has no solution. Therefore, the correct answer is: “The system has no solution.” The system does not have a unique solution or infinitely many solutions.