\[ \left\{\begin{array}{c}2 x+2 y=-12 \\ x-2 y=6\end{array}\right. \] 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.

Evaluate the expression by following steps: - step0: Evaluate: \(2x+2y\) - step1: Substitute: \(2\times 2+2\left(-2\right)\) - step2: Multiply the numbers: \(4+2\left(-2\right)\) - step3: Multiply the numbers: \(4-4\) - step4: Subtract the numbers: \(0\) Substitute \( x=2,y=-2 \) into the expression \( x - 2y \). Evaluate the expression by following steps: - step0: Evaluate: \(x-2y\) - step1: Substitute: \(2-2\left(-2\right)\) - step2: Multiply the numbers: \(2+4\) - step3: Add the numbers: \(6\) To determine if the point \( (2, -2) \) lies on both lines represented by the equations in the system, we will substitute \( x = 2 \) and \( y = -2 \) into each equation. 1. **First Equation:** \[ 2x + 2y = -12 \] Substituting \( x = 2 \) and \( y = -2 \): \[ 2(2) + 2(-2) = 4 - 4 = 0 \] The left side equals \( 0 \), which does not equal \( -12 \). Therefore, the point does not satisfy the first equation. 2. **Second Equation:** \[ x - 2y = 6 \] Substituting \( x = 2 \) and \( y = -2 \): \[ 2 - 2(-2) = 2 + 4 = 6 \] The left side equals \( 6 \), which matches the right side. Therefore, the point satisfies the second equation. ### Conclusion: The point \( (2, -2) \) does not lie on the first line but does lie on the second line. Thus, it does not lie on both lines in the system of equations.