Question

Is (9, 2) a solution to this system of inequalities?

x + 4y < 19
x > 8

Answer 1

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.

1. 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.

2. 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.