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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?

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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.

Tell whether the ordered pair (-4,2) is a solution of the system of linear inequalities:

1. y < -4x
2. y ≥ x - 4

Check if the ordered pair (-4,2) satisfies the system of linear inequalities y < -4x and y ≥ x - 4. This problem covers key algebraic concepts including substitution and inequality validation. Suitable for students in Grades 7-9.

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