Question: System B \[ 2x - y = -6 \] \[ -2x + y = -6 \] The system has no solution. The system has a…

System B

\[ 2x - y = -6 \] \[ -2x + y = -6 \]

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

To solve the given system of equations, we will analyze the equations for consistency and possible solutions. The system is: \[ \begin{cases} 2x - y = -6 & \\ -2x + y = -6 & \end{cases} \] Add the two equations to eliminate \(x\) and \(y\): \[ (2x - y) + (-2x + y) = -6 + (-6) \] Simplify: \[ 0 = -12 \] Since \(0 = -12\) is a contradiction, this means the system has no solution. Therefore, the correct choice is: - The system has no solution.