Question

Is (2, 1) a solution to this system of inequalities?

y > –1/2x − 6
y > 1/2x − 1

Answer 1

To determine if the point (2, 1) is a solution to the system of inequalities, we will substitute \( x = 2 \) and \( y = 1 \) into each inequality and check if both inequalities are satisfied.

1. **First inequality:**
\[
y > -\frac{1}{2}x - 6
\]
Substituting \( x = 2 \) and \( y = 1 \):
\[
1 > -\frac{1}{2}(2) - 6
\]
\[
1 > -1 - 6
\]
\[
1 > -7
\]
This inequality is true.

2. **Second inequality:**
\[
y > \frac{1}{2}x - 1
\]
Substituting \( x = 2 \) and \( y = 1 \):
\[
1 > \frac{1}{2}(2) - 1
\]
\[
1 > 1 - 1
\]
\[
1 > 0
\]
This inequality is also true.

Since both inequalities are satisfied, we can conclude that the point (2, 1) is indeed a solution to the system of inequalities.