Question

which of the following inequalities is (2,2) a solution?
SELECT ALL THAT APPLY
a y < -2x + 1
b y > 3x - 2
c y > x - 1

Answer 1

To determine which inequalities the point (2, 2) satisfies, we will substitute \(x = 2\) and \(y = 2\) into each inequality and check if the inequality holds.

### a) \(y < -2x + 1\)

Substituting \(x = 2\) and \(y = 2\):

\[
2 < -2(2) + 1
\]

Calculating the right side:

\[
-2(2) + 1 = -4 + 1 = -3
\]

So the inequality is:

\[
2 < -3 \quad \text{(False)}
\]

### b) \(y > 3x - 2\)

Substituting \(x = 2\) and \(y = 2\):

\[
2 > 3(2) - 2
\]

Calculating the right side:

\[
3(2) - 2 = 6 - 2 = 4
\]

So the inequality is:

\[
2 > 4 \quad \text{(False)}
\]

### c) \(y > x - 1\)

Substituting \(x = 2\) and \(y = 2\):

\[
2 > 2 - 1
\]

Calculating the right side:

\[
2 - 1 = 1
\]

So the inequality is:

\[
2 > 1 \quad \text{(True)}
\]

### Conclusion
The only inequality that (2, 2) satisfies is:

**c) \(y > x - 1\)**

So the answer is **c only**.