Question

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

A: y< -2x + 1

B: y is greater than or equal to 3x - 2

C: y > x - 1

Answer 1

To determine if the point (2, 2) is a solution to each of the inequalities, we will substitute \( x = 2 \) and \( y = 2 \) into each inequality and see if it holds true.

**A: \( y < -2x + 1 \)**
Substituting:
\[
2 < -2(2) + 1 \\
2 < -4 + 1 \\
2 < -3
\]
This is **false**, so (2, 2) is not a solution to inequality A.

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**B: \( y \geq 3x - 2 \)**
Substituting:
\[
2 \geq 3(2) - 2 \\
2 \geq 6 - 2 \\
2 \geq 4
\]
This is **false**, so (2, 2) is not a solution to inequality B.

---

**C: \( y > x - 1 \)**
Substituting:
\[
2 > 2 - 1 \\
2 > 1
\]
This is **true**, so (2, 2) is a solution to inequality C.

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**Conclusion:**
The only inequality for which (2, 2) is a solution is **C: \( y > x - 1 \)**.