Decide whether the ordered pair \( (6,-6) \) is a solution of the system of equations. \( \left\{\begin{array}{l}2 x+y=6 \\ 4 x+2 y=12\end{array}\right. \)

To determine whether the ordered pair \((6, -6)\) is a solution to the system of equations: \[ \left\{ \begin{array}{l} 2x + y = 6 \\ 4x + 2y = 12 \end{array} \right. \] we need to substitute \(x = 6\) and \(y = -6\) into both equations and check if both are satisfied. **1. Substitute into the first equation:** \[ 2x + y = 6 \] \[ 2(6) + (-6) = 12 - 6 = 6 \] \[ 6 = 6 \quad \text{✓} \] The first equation is satisfied. **2. Substitute into the second equation:** \[ 4x + 2y = 12 \] \[ 4(6) + 2(-6) = 24 - 12 = 12 \] \[ 12 = 12 \quad \text{✓} \] The second equation is also satisfied. **Conclusion:** Since the ordered pair \((6, -6)\) satisfies both equations in the system, it **is** a solution to the system. **Final Answer:** Yes, the ordered pair \( (6, -6) \) satisfies both equations and is a solution to the system.