Is (-3,-4) a solution to this system of inequalities? 10x-10y<10 and 19x-11y<-13 yes or no?

Let's check if the point \((-3, -4)\) satisfies both inequalities in the system.

### First inequality: 
\[ 10x - 10y < 10 \]
Substitute \( x = -3 \) and \( y = -4 \):
\[
10(-3) - 10(-4) < 10 
\]
\[
-30 + 40 < 10 
\]
\[
10 < 10 
\]
This is **false** because 10 is not less than 10.

Since the point \((-3, -4)\) does not satisfy the first inequality, it is **not a solution** to the system of inequalities.

### Final Answer: No, \((-3, -4)\) is not a solution.

Would you like further details on this solution or have any questions?

Here are 5 related questions to deepen your understanding:
1. How do you solve systems of inequalities graphically?
2. What happens if a point satisfies only one inequality in the system?
3. Can systems of inequalities have more than one solution?
4. How do systems of linear inequalities differ from systems of linear equations?
5. What are the applications of systems of inequalities in real-world problems?

**Tip:** When checking if a point is a solution, always test it in each inequality individually!

Determine whether the point (-3, -4) satisfies the system of inequalities 10x-10y<10 and 19x-11y<-13. This detailed step-by-step solution uses substitution to check each inequality individually. Ideal for students in Grades 9-10 learning about linear inequalities.

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