To determine if the point \( (3, 5) \) is a solution to the system of inequalities given by:
- \( y < x + 6 \)
- \( y < 9x + 8 \)
we need to substitute \( x = 3 \) and \( y = 5 \) into both inequalities.
Checking the first inequality:
Substituting into \( y < x + 6 \):
\[ 5 < 3 + 6 \] \[ 5 < 9 \]
This is true.
Checking the second inequality:
Substituting into \( y < 9x + 8 \):
\[ 5 < 9(3) + 8 \] \[ 5 < 27 + 8 \] \[ 5 < 35 \]
This is also true.
Since both inequalities hold true for the point \( (3, 5) \), we conclude that \( (3, 5) \) is indeed a solution to the system of inequalities.