Question

Which ordered pair is a solution to this system of inequalities

−2x−x≥6

y≥−6

x≥−8

(1 point)
Responses

(-6,-8)
(-6,-8)

(2, -6)
(2, -6)

(-10, -6)
(-10, -6)

(-6, -6)

Answer 1

To determine which ordered pair is a solution to the system of inequalities, let's analyze each inequality step by step:

1. The first inequality is \( -2x - x \geq 6 \) which simplifies to \( -3x \geq 6 \). Dividing both sides by -3 (and flipping the inequality sign) gives us \( x \leq -2 \).

2. The second inequality is \( y \geq -6 \).

3. The third inequality is \( x \geq -8 \).

Now we have the simplified system:
1. \( x \leq -2 \)
2. \( y \geq -6 \)
3. \( x \geq -8 \)

Now we can check each ordered pair given in the options to see if they satisfy all three inequalities.

**Check (-6, -8)**:
- \( x = -6 \) → satisfies \( x \leq -2 \) and \( x \geq -8 \).
- \( y = -8 \) → does NOT satisfy \( y \geq -6 \).

**Check (2, -6)**:
- \( x = 2 \) → does NOT satisfy \( x \leq -2 \).

**Check (-10, -6)**:
- \( x = -10 \) → satisfies \( x \leq -2 \) and \( x \geq -8 \) because -10 is less than -8.
- \( y = -6 \) → satisfies \( y \geq -6 \). (Note: for \( y \) it should be strictly greater than or equal to -6).

**Check (-6, -6)**:
- \( x = -6 \) → satisfies \( x \leq -2 \) and \( x \geq -8 \).
- \( y = -6 \) → satisfies \( y \geq -6 \).

From our checks:
- (-6, -8) does not work.
- (2, -6) does not work.
- (-10, -6) does not work because -10 does not satisfy \( x \geq -8 \).
- (-6, -6) works.

Therefore, the correct answer is **(-6, -6)**.