Question

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

y≥−12x+6
𝑦
≥
−
1
2
𝑥
+
6

y<4
𝑦
<
4

Enter 1 for YES

Enter 2 for NO

Answer 1

To determine if the point (10, 2) is a solution to the system of inequalities, we will first understand the inequalities and then test the point against each one.

1. **First Inequality:**
\[
y \geq -12x + 6
\]
Substituting (10, 2):
\[
2 \geq -12(10) + 6 \implies 2 \geq -120 + 6 \implies 2 \geq -114
\]
This is true.

2. **Second Inequality:**
\[
y \geq -\frac{1}{2}x + 6
\]
Substituting (10, 2):
\[
2 \geq -\frac{1}{2}(10) + 6 \implies 2 \geq -5 + 6 \implies 2 \geq 1
\]
This is also true.

3. **Third Inequality:**
\[
y < 4
\]
Substituting (10, 2):
\[
2 < 4
\]
This is true as well.

Since the point (10, 2) satisfies all three inequalities, it is indeed a solution to the system.

Therefore, the answer is:
**1 for YES**.