1. If the sound system hadn't failed,last night's show would have been better

a. this is a correct sentence using the 1st conditional form
b. this is correct sentence using the 2nd conditional form
C. this is a correct sentence using the 3rd conditional form
answer A
2. They'll work on new songs tomorrow if they would have time
a. this is an incorrect sentence
b. this is a correct sentence using the 1st conditional form
c. this is a correct sentence using the 2nd conditional form
Answer a
3. If the clubs's manager agrees, they'll play a few more original songs tomorrow
a. this is correct using the 1st conditional form
b. this is correct using the 2nd conditional form
c. this is correct using the 3rd conditional form
Answer b
4. the duo could perform at weddinds in mike played the flute
a. this correct using 1st conditional
b. this is correct using the 2nd conditional
c. this correct using the 3rd conditional
Answer c

1 is "c"

The third conditional or past unreal conditional describes a condition that can not be met because the opportunity is past.

When did the system fail? It failed in the past, last night.

Please re-think these, using the information here:

http://grammar.ccc.commnet.edu/grammar/conditional2.htm

#2 - the only correct one

3 and 4 are now correct.

1 still is not.

1. c.

3. a.
4. b.

1. If the sound system hadn't failed, last night's show would have been better.

- This is a correct sentence using the 3rd conditional form.

To determine the form of the conditional sentence, we look at the structure "If + subject + past perfect, subject + would + have + past participle." In this sentence, "If the sound system hadn't failed" is the conditional clause, which uses the past perfect tense (hadn't failed). The result clause "last night's show would have been better" uses "would have + past participle," indicating a hypothetical outcome in the past. Therefore, this sentence is in the 3rd conditional form.

2. They'll work on new songs tomorrow if they would have time.
- This is an incorrect sentence.

The sentence is incorrect because it combines tenses in a way that doesn't follow the rules of conditional statements. The conditional clause "if they would have time" should use the simple present tense "if they have time" to indicate a condition in the future. Thus, the correct form of this sentence would be: "They'll work on new songs tomorrow if they have time."

3. If the club's manager agrees, they'll play a few more original songs tomorrow.
- This is a correct sentence using the 2nd conditional form.

To determine the form of the conditional sentence, we look at the structure "If + subject + simple past, subject + would + base form of the verb." In this sentence, "If the club's manager agrees" is the conditional clause, which uses the simple past tense (agrees). The result clause "they'll play a few more original songs tomorrow" uses "would + base form of the verb," indicating a hypothetical action in the future. Therefore, this sentence is in the 2nd conditional form.

4. The duo could perform at weddings if Mike played the flute.
- This is a correct sentence using the 2nd conditional form.

To determine the form of the conditional sentence, we look at the structure "If + subject + simple past, subject + would + base form of the verb." In this sentence, "If Mike played the flute" is the conditional clause, which uses the simple past tense (played). The result clause "the duo could perform at weddings" uses "would + base form of the verb," indicating a hypothetical action in the present or future. Therefore, this sentence is in the 2nd conditional form.