Is (1,-1) a solution to this system of inequalities? 11x+16y<-16 and 6x-y<7 yes or no?

Let's check if the point \((1, -1)\) satisfies both inequalities.

### 1. First inequality: \(11x + 16y < -16\)
Substitute \(x = 1\) and \(y = -1\) into the inequality:
\[
11(1) + 16(-1) < -16
\]
\[
11 - 16 < -16
\]
\[
-5 < -16
\]
This is **false** because \(-5\) is not less than \(-16\).

Since the point does not satisfy the first inequality, it is **not** a solution to the system of inequalities.

The answer is **no**.

Would you like further clarification on this? Here are five questions to explore related concepts:
1. What are the basic methods for solving systems of inequalities?
2. How do you graph a system of inequalities?
3. Can a system of inequalities have no solutions? Why or why not?
4. How do you verify a solution to a system of inequalities graphically?
5. What are some real-life applications of systems of inequalities?

**Tip:** When checking solutions to inequalities, always substitute the values and carefully compare the results to the inequality sign!

Check if the point (1,-1) satisfies the system of inequalities 11x + 16y < -16 and 6x - y < 7. This problem explores key algebraic concepts, including systems of inequalities and substitution. Suitable for students in Grades 8-10.

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