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.