\( \begin{array}{l}x-3 y=2 \\ -x-6 y=-11 \\ \text { Is }(5,1) \text { a solution to the system above? } \bigcirc \text { True False } \\ \text { Submit Question }\end{array} \)

To check if the point (5,1) is a solution to the given system of equations, we need to substitute \(x = 5\) and \(y = 1\) into both equations. 1. For the first equation \(x - 3y = 2\): \[ 5 - 3(1) = 5 - 3 = 2 \quad \text{(True)} \] 2. For the second equation \(-x - 6y = -11\): \[ -5 - 6(1) = -5 - 6 = -11 \quad \text{(True)} \] Since both equations hold true with the given point, the answer is **True**. Additionally, when checking if a point is a solution to a system of equations, it's crucial to substitute it into every equation. Often, students might stop after checking one equation, but a careful check on all equations ensures accurate validation of solutions!