To determine if the point (2, -6) is a solution to the system of inequalities, we will substitute \( x = 2 \) and \( y = -6 \) into both inequalities.
- For the first inequality:
\[ y \geq \frac{1}{2}x - 7 \]
Substituting \( x = 2 \) and \( y = -6 \):
\[ -6 \geq \frac{1}{2}(2) - 7 \]
Calculating the right side:
\[ -6 \geq 1 - 7 \] \[ -6 \geq -6 \]
This inequality is true.
- For the second inequality:
\[ y \leq -8 \]
Substituting \( y = -6 \):
\[ -6 \leq -8 \]
This inequality is false.
Since the point (2, -6) satisfies the first inequality but does not satisfy the second inequality, it is not a solution to the system of inequalities.
Thus, the answer is no, (2, –6) is not a solution to this system of inequalities.