Question

Graph the system of inequalities and determine if the point (10,2) is a solution.

y
≥
−
1
2
x
+
6


y
<
4


Enter 1 for YES

Enter 2 for NO

(1 point)

Answer 1

To determine if the point (10,2) is a solution to the given system of inequalities, we will check each inequality one by one.

1. **First Inequality:** \( y \geq -\frac{1}{2}x + 6 \)

Substitute \( x = 10 \) and \( y = 2 \):

\[
2 \geq -\frac{1}{2}(10) + 6
\]

\[
2 \geq -5 + 6
\]

\[
2 \geq 1
\]

This is true, so (10,2) satisfies the first inequality.

2. **Second Inequality:** \( y < 4 \)

Substitute \( y = 2 \):

\[
2 < 4
\]

This is also true, so (10,2) satisfies the second inequality.

Since (10,2) satisfies both inequalities, it is a solution to the system.

**Enter 1 for YES.**