Question

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

6x + y > 13
4x + 9y ≤ 19

Answer 1

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

1. For the first inequality:

\[
6x + y > 13
\]

Substituting \( x = 2 \) and \( y = 1 \):

\[
6(2) + 1 > 13
\]

Calculating:

\[
12 + 1 > 13 \implies 13 > 13
\]

This is **not true**, so the point (2, 1) does not satisfy the first inequality.

2. For the second inequality:

\[
4x + 9y ≤ 19
\]

Substituting \( x = 2 \) and \( y = 1 \):

\[
4(2) + 9(1) ≤ 19
\]

Calculating:

\[
8 + 9 ≤ 19 \implies 17 ≤ 19
\]

This is **true**, so the point (2, 1) satisfies the second inequality.

Since (2, 1) does not satisfy the first inequality, it is **not a solution** to the system of inequalities.