Question

Is (6, –9) a solution to this system of inequalities?
y <= -(1)/(2)x-7
y<-(1)/(6)x-5

Answer 1

To determine whether the point (6, -9) is a solution to the system of inequalities, we need to check if it satisfies each inequality.

1. **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**.

2. **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**.