Which ordered pairs are solutions to the inequality 2y−x≤−6?

Question

Select each correct answer.



Responses

(−3, 0)
begin ordered pair negative 3 comma 0 end ordered pair

(1, −4)
begin ordered pair 1 comma negative 4 end ordered pair

(2, −2)
begin ordered pair 2 comma negative 2 end ordered pair

(6, 1)
begin ordered pair 6 comma 1 end ordered pair

(0, −3)

Answer 1

To determine which ordered pairs are solutions to the inequality \(2y - x \leq -6\), we can substitute each pair into the inequality and see if it holds true.

1. For the pair \((-3, 0)\): \[ 2(0) - (-3) = 0 + 3 = 3 \quad \text{(not valid since \(3 \not\leq -6\))} \]

2. For the pair \((1, -4)\): \[ 2(-4) - 1 = -8 - 1 = -9 \quad \text{(valid since \(-9 \leq -6\))} \]

3. For the pair \((2, -2)\): \[ 2(-2) - 2 = -4 - 2 = -6 \quad \text{(valid since \(-6 \leq -6\))} \]

4. For the pair \((6, 1)\): \[ 2(1) - 6 = 2 - 6 = -4 \quad \text{(not valid since \(-4 \not\leq -6\))} \]

5. For the pair \((0, -3)\): \[ 2(-3) - 0 = -6 - 0 = -6 \quad \text{(valid since \(-6 \leq -6\))} \]

Based on these calculations, the ordered pairs that are solutions to the inequality \(2y - x \leq -6\) are:

• \((1, -4)\)
• \((2, -2)\)
• \((0, -3)\)