Bot GPT 4-o mini To determine whether the point (6, -9) is a solution to the system of inequalities, we need to check if it satisfies each inequality.
-
First inequality: \( y \leq -\frac{1}{2}x - 7 \)
Substitute \( x = 6 \) and \( y = -9 \) into the inequality: \[ -9 \leq -\frac{1}{2}(6) - 7 \] \[ -9 \leq -3 - 7 \] \[ -9 \leq -10 \] This is false.
-
Second inequality: \( y < -\frac{1}{6}x - 5 \)
Again, substitute \( x = 6 \) and \( y = -9 \): \[ -9 < -\frac{1}{6}(6) - 5 \] \[ -9 < -1 - 5 \] \[ -9 < -6 \] This is true.
Since the point (6, -9) does not satisfy the first inequality (it is false) but satisfies the second inequality, we conclude that (6, -9) is not a solution to the system of inequalities.
1 answer