Question

Is (1, 6) a solution to this system of inequalities?

2x + 3y ≥ 20
x + 2y < 13

Answer 1

To determine if the point (1, 6) is a solution to the system of inequalities, we will substitute \( x = 1 \) and \( y = 6 \) into each inequality and check if it satisfies them.

1. For the first inequality:
\[
2x + 3y ≥ 20
\]
Substituting \( x = 1 \) and \( y = 6 \):
\[
2(1) + 3(6) ≥ 20
\]
\[
2 + 18 ≥ 20
\]
\[
20 ≥ 20
\]
This inequality is **satisfied**.

2. For the second inequality:
\[
x + 2y < 13
\]
Substituting \( x = 1 \) and \( y = 6 \):
\[
1 + 2(6) < 13
\]
\[
1 + 12 < 13
\]
\[
13 < 13
\]
This inequality is **not satisfied** (it is false).

Since (1, 6) satisfies the first inequality but not the second, it is **not a solution** to the system of inequalities.