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