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.
- 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.
- 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.