Question

Is (3, 5) a solution to this system of inequalities?

y < x + 6
y < 9x + 8

Answer 1

To determine if the point \( (3, 5) \) is a solution to the system of inequalities given by:

1. \( y < x + 6 \)
2. \( y < 9x + 8 \)

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.