To determine if the ordered pair $(-4, 2)$ is a solution to the system of linear inequalities:

1. $y < -4x$
2. $y \geq x - 4$

we substitute $x = -4$ and $y = 2$ into each inequality and check if both are true.

Step 1: Check the first inequality $y < -4x$

Substitute $x = -4$ and $y = 2$ into $y < -4x$:

$2 < -4(-4)$ $2 < 16$

This is true, so the ordered pair $(-4, 2)$ satisfies the first inequality.

Step 2: Check the second inequality $y \geq x - 4$

Substitute $x = -4$ and $y = 2$ into $y \geq x - 4$:

$2 \geq -4 - 4$ $2 \geq -8$

This is also true, so the ordered pair $(-4, 2)$ satisfies the second inequality as well.

Conclusion

Since $(-4, 2)$ satisfies both inequalities, it is a solution to the system of linear inequalities.

Would you like more details, or do you have any questions?

Here are some related questions for further practice:

1. How would you determine if a different point is a solution to this system?
2. What would happen if one of the inequalities used $\leq$ or $>$ instead?
3. Can you graph these inequalities to visually confirm the solution?
4. How do we know when a system of inequalities has no solutions?
5. How would you test multiple points in one system of inequalities?

Tip: Always substitute each inequality separately to ensure accuracy when verifying solutions.