#13.

Which of the following inequalities is
(2,2) a solution?

(Select all that apply.)

y<−2x+1

y≥3x−2

y>x−1

1 answer

To determine whether the point (2, 2) is a solution to each of the inequalities, we can substitute \(x = 2\) and \(y = 2\) into each inequality and check their validity.

  1. For the inequality \(y < -2x + 1\):

    Substitute \(x = 2\) and \(y = 2\): \[ 2 < -2(2) + 1 \] \[ 2 < -4 + 1 \] \[ 2 < -3 \quad \text{(False)} \]

  2. For the inequality \(y \ge 3x - 2\):

    Substitute \(x = 2\) and \(y = 2\): \[ 2 \ge 3(2) - 2 \] \[ 2 \ge 6 - 2 \] \[ 2 \ge 4 \quad \text{(False)} \]

  3. For the inequality \(y > x - 1\):

    Substitute \(x = 2\) and \(y = 2\): \[ 2 > 2 - 1 \] \[ 2 > 1 \quad \text{(True)} \]

The only inequality for which (2, 2) is a solution is:

  • \(y > x - 1\)

Thus, the answer to which inequalities have (2, 2) as a solution is:

  • \(y > x - 1\)