Is (-4,-2) a solution to this system of inequalities? 2x-7y<14 ans 4x-y>14 yes or no?

To determine if \((-4,-2)\) is a solution to the system of inequalities:

1. **Inequality 1**: \(2x - 7y < 14\)
   - Substitute \(x = -4\) and \(y = -2\):
   \[
   2(-4) - 7(-2) = -8 + 14 = 6
   \]
   Since \(6 < 14\), this inequality is true.

2. **Inequality 2**: \(4x - y > 14\)
   - Substitute \(x = -4\) and \(y = -2\):
   \[
   4(-4) - (-2) = -16 + 2 = -14
   \]
   Since \(-14\) is not greater than \(14\), this inequality is false.

Since the second inequality is false, \((-4, -2)\) is **not** a solution to the system.

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you graph systems of inequalities?
2. What are the steps to check solutions for systems of inequalities?
3. How do you interpret the solution region of a system of inequalities?
4. Can a point satisfy one inequality but not the other in a system?
5. How do you solve systems of inequalities algebraically?

**Tip:** Always substitute both \(x\) and \(y\) values into each inequality to verify if a point satisfies the system.

Is (-4,-2) a solution to this system of inequalities? 2x - 7y < 14 and 4x - y > 14, yes or no?

Check if the point (-4, -2) is a solution to the system of inequalities 2x - 7y < 14 and 4x - y > 14. This detailed explanation covers substitution method, algebraic concepts, and how to verify solutions for systems of inequalities. Suitable for students in Grades 8-10.

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