Does the point (5,1) satisfy the inequality 9x+16y>14?

To determine whether the point \((5, 1)\) satisfies the inequality \(9x + 16y > 14\), we will substitute the values \(x = 5\) and \(y = 1\) into the inequality and check the result.

### Substitution:
\[
9(5) + 16(1) > 14
\]
\[
45 + 16 > 14
\]
\[
61 > 14
\]

Since \(61\) is indeed greater than \(14\), the point \((5, 1)\) **satisfies** the inequality.

Would you like more details or have any other questions?

Here are 5 related questions to explore further:
1. How do you determine if a point satisfies a system of inequalities?
2. Can you graph the inequality \(9x + 16y > 14\) and show the solution region?
3. What would happen if the inequality was \(9x + 16y \leq 14\)?
4. How do you solve for \(x\) and \(y\) if the inequality was instead an equation, \(9x + 16y = 14\)?
5. What is the geometric interpretation of the inequality \(9x + 16y > 14\)?

**Tip:** Always plug in the coordinates of the point into the inequality to test whether it satisfies the condition.

Explore whether the point (5,1) satisfies the inequality 9x + 16y > 14 by substituting the coordinates into the inequality. This solution covers essential algebraic concepts such as substitution and properties of inequalities. Suitable for students in Grades 6-8.

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