Question: The system has no solution. The system has a unique solution: \[ (x, y) = (\boxed{\phantom{0}},…

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

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

Solution

To solve System B: \[ \begin{cases} 2x - y = -6 & \\ -2x + y = -6 & \end{cases} \] First, add the two equations together to eliminate \(y\): \[ (2x - y) + (-2x + y) = -6 + (-6) \] Simplify the equation: \[ 0 = -12 \] Since \(0 = -12\) is a contradiction, the system has no solution. Thus, the correct choice is: “The system has no solution.”