Question

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

x + 8y ≥ 19
x > 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.

1. **First Inequality:** \( x + 8y ≥ 19 \)

Substitute \( x = 2 \) and \( y = 1 \):
\[
2 + 8(1) ≥ 19
\]
\[
2 + 8 ≥ 19
\]
\[
10 ≥ 19
\]
This inequality is **not true**.

2. **Second Inequality:** \( x > 1 \)

Substitute \( x = 2 \):
\[
2 > 1
\]
This inequality is **true**.

Since the first inequality is not satisfied, the point (2, 1) is **not a solution** to the system of inequalities.