Question

A student wrote the inequality y < 2z-3. Her friend solved the inequality and said that (2, 1) is one of the possible solutions of this inequality. Is her friend correct?

No, because 1 is greater than 2 (2) -3.

O Yes, because 1 is equal to 2 (2)

No, because 1 is equal to 2 (2) -3.

Yes, because 1 is greater than 2 (2) -3.

Answer 1

To determine if the point (2, 1) is a solution to the inequality \( y < 2z - 3 \), we need to substitute \( z = 1 \) and see if the inequality holds.

The inequality is:
\[ y < 2z - 3. \]

Substituting \( z = 1 \):
\[ y < 2(1) - 3 \]
\[ y < 2 - 3 \]
\[ y < -1. \]

Now we substitute \( y = 2 \) (the first value in the point (2, 1)):
\[ 2 < -1. \]

This statement is false. Thus, the point (2, 1) does not satisfy the inequality \( y < 2z - 3 \).

Now let's evaluate the options provided:

1. **No, because 1 is greater than 2 (2) - 3.** (Incorrect reasoning)
2. **Yes, because 1 is equal to 2 (2).** (Incorrect reasoning)
3. **No, because 1 is equal to 2 (2) - 3.** (Incorrect reasoning)
4. **Yes, because 1 is greater than 2 (2) - 3.** (Incorrect reasoning)

Since none of the provided options correctly explain why (2, 1) is not a solution, the correct response would simply be:

**No, (2, 1) is not a solution of the inequality.**