To determine if the point (9, 2) is a solution to the system of inequalities, we need to substitute \(x = 9\) and \(y = 2\) into each inequality and check if they hold true.
- For the first inequality:
\[ x + 4y < 19 \]
Substituting in \(x = 9\) and \(y = 2\):
\[ 9 + 4(2) < 19 \] \[ 9 + 8 < 19 \] \[ 17 < 19 \]
This inequality is true.
- For the second inequality:
\[ x > 8 \]
Substituting in \(x = 9\):
\[ 9 > 8 \]
This inequality is also true.
Since both inequalities are satisfied by the point (9, 2), we can conclude that (9, 2) is a solution to the given system of inequalities.