Question

Is (–6, 10) a solution to this system of inequalities?
y > -1/6x + 8
y > 1/2x - 6

A) yes
B) no

Answer 1

To determine if the point (–6, 10) is a solution to the system of inequalities, we need to substitute \(x = -6\) and \(y = 10\) into each inequality and see if both are satisfied.

1. For the first inequality:
\[
y > -\frac{1}{6}x + 8
\]
Substituting \(x = -6\) and \(y = 10\):
\[
10 > -\frac{1}{6}(-6) + 8
\]
Calculate \(-\frac{1}{6}(-6) + 8\):
\[
-\frac{1}{6}(-6) = 1 \quad \Rightarrow \quad 1 + 8 = 9
\]
Thus, the inequality becomes:
\[
10 > 9
\]
This is true.

2. For the second inequality:
\[
y > \frac{1}{2}x - 6
\]
Substituting \(x = -6\) and \(y = 10\):
\[
10 > \frac{1}{2}(-6) - 6
\]
Calculate \(\frac{1}{2}(-6) - 6\):
\[
\frac{1}{2}(-6) = -3 \quad \Rightarrow \quad -3 - 6 = -9
\]
Thus, the inequality becomes:
\[
10 > -9
\]
This is also true.

Since (–6, 10) satisfies both inequalities, the answer is:

A) yes.