\[ \left\{\begin{array}{c}2 x+2 y=-12 \\ x-2 y=6\end{array}\right. \] Determine if the point \( (2,-2) \) lies on both of the lines in the system of equations by substituting the ordefed pair into both equations.

To determine if the point \( (2, -2) \) lies on both lines represented by the equations in the system, we need to substitute \( x = 2 \) and \( y = -2 \) into both equations. For the first equation \( 2x + 2y = -12 \): \[ 2(2) + 2(-2) = 4 - 4 = 0 \neq -12 \] For the second equation \( x - 2y = 6 \): \[ 2 - 2(-2) = 2 + 4 = 6 \] The point \( (2, -2) \) satisfies the second equation but not the first one. Therefore, it does not lie on both lines. Alternatively, you could graph the equations to visually confirm the intersection or lack thereof. Graphing them can reveal how they meet (or don't) in the coordinate plane, turning numbers into a picture—sometimes, that's how you can more easily see relationships!