Which of the following inequalities is `(2,2)` a solution? (Select all that apply.)

Question

y<-2x+1
y ≥ 3x-2
y>x-1

Answer 1

To determine which inequalities the point (2, 2) is a solution for, we can substitute \(x = 2\) and \(y = 2\) into each inequality.

1. Inequality: \(y < -2x + 1\)

   • Substitute \(x = 2\) and \(y = 2\):
   • \(2 < -2(2) + 1\)
   • \(2 < -4 + 1\)
   • \(2 < -3\) (FALSE)

2. Inequality: \(y \geq 3x - 2\)

   • Substitute \(x = 2\) and \(y = 2\):
   • \(2 \geq 3(2) - 2\)
   • \(2 \geq 6 - 2\)
   • \(2 \geq 4\) (FALSE)

3. Inequality: \(y > x - 1\)

   • Substitute \(x = 2\) and \(y = 2\):
   • \(2 > 2 - 1\)
   • \(2 > 1\) (TRUE)

So, the only inequality that (2, 2) satisfies is \(y > x - 1\).

Final Answer:

• \(y > x - 1\) is the only inequality where (2, 2) is a solution.