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Which ordered pairs are solutions to the inequality y−4x≥−5?

Select each correct answer.



Responses

(−2, 1)
begin ordered pair negative 2 comma 1 end ordered pair

(4, 0)
begin ordered pair 4 comma 0 end ordered pair

(−4, 2)
begin ordered pair negative 4 comma 2 end ordered pair

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

(5, −2)

1 answer

To determine which ordered pairs are solutions to the inequality \( y - 4x \ge -5 \), we can rearrange the inequality into a more convenient form:

\[ y \ge 4x - 5 \]

Next, we will substitute each ordered pair \((x, y)\) into the inequality to check if it holds true.

  1. For \((-2, 1)\): \[ y = 1, \quad 4x - 5 = 4(-2) - 5 = -8 - 5 = -13 \] Since \(1 \ge -13\) (true), \((-2, 1)\) is a solution.

  2. For \((4, 0)\): \[ y = 0, \quad 4x - 5 = 4(4) - 5 = 16 - 5 = 11 \] Since \(0 \ge 11\) (false), \((4, 0)\) is not a solution.

  3. For \((-4, 2)\): \[ y = 2, \quad 4x - 5 = 4(-4) - 5 = -16 - 5 = -21 \] Since \(2 \ge -21\) (true), \((-4, 2)\) is a solution.

  4. For \((1, -1)\): \[ y = -1, \quad 4x - 5 = 4(1) - 5 = 4 - 5 = -1 \] Since \(-1 \ge -1\) (true), \((1, -1)\) is a solution.

  5. For \((5, -2)\): \[ y = -2, \quad 4x - 5 = 4(5) - 5 = 20 - 5 = 15 \] Since \(-2 \ge 15\) (false), \((5, -2)\) is not a solution.

Thus, the ordered pairs that are solutions to the inequality \( y - 4x \ge -5 \) are:

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