Which point would not be a solution to the system of linear inequalities shown below? \[ y>3 x-7 \quad y \geq-x-1 \] Answer \( (-2,9) \)

To determine whether the point \((-2, 9)\) is a solution to the system of linear inequalities given by: 1. \( y > 3x - 7 \) 2. \( y \geq -x - 1 \) we will substitute \(x = -2\) and \(y = 9\) into each inequality and check if the point satisfies both. ### Step 1: Check the first inequality Substituting into the first inequality: \[ y > 3x - 7 \] Substituting \(x = -2\) and \(y = 9\): \[ 9 > 3(-2) - 7 \] Calculating the right side: \[ 9 > -6 - 7 \] \[ 9 > -13 \] This inequality is true. ### Step 2: Check the second inequality Now, substituting into the second inequality: \[ y \geq -x - 1 \] Substituting \(x = -2\) and \(y = 9\): \[ 9 \geq -(-2) - 1 \] Calculating the right side: \[ 9 \geq 2 - 1 \] \[ 9 \geq 1 \] This inequality is also true. ### Conclusion Since the point \((-2, 9)\) satisfies both inequalities, it is indeed a solution to the system of linear inequalities. To find a point that does not satisfy the system, we can check other points or analyze the inequalities further. Would you like to check another specific point or find a point that does not satisfy the inequalities?