回答 and 解答: replies and problem answers with the same reading
Choose between the two forms pronounced かいとう by the function of an inquiry response or problem answer, keeping correctness a separate issue.
Responding to an inquiry or survey
「質問への回答を金曜日までに送ってください。」 requests a reply to the question by Friday. 回答 names the response, while the request does not establish that it was sent.
「アンケートに回答した人へ礼状を出した。」 describes sending thank-you notes to people who answered a survey. It identifies survey-response roles rather than evaluating every response as correct.
Answers and reasoning for a problem
「試験が終わってから、友達と解答を確かめ合った。」 describes checking test answers with a friend after the test. 解答 identifies the answers to the problems, and checking them does not itself state a correctness judgment.
「先生は正解だけでなく、解答に至る考え方も説明した。」 describes the teacher explaining the reasoning toward an answer as well as the correct answer. Read the roles of 正解 and the process leading to 解答 separately.
Choose the written form by its function
回答 and 解答 share the reading かいとう. Their focus differs between responding to an inquiry or survey and providing an answer or reasoning for a problem. Identify the function instead of choosing from sound alone.
Neither written form guarantees correctness. Identify whether the content responds to an inquiry or answers a problem, then read any separate statement about correctness.
Which form fits a survey response and which fits test answers checked with a friend? Does either form establish a correct answer?
Show the answer and why
回答 fits the survey response, and 解答 fits the test-problem answers. They have the same reading but different response functions. Correctness remains separate, and merely checking a 解答 does not establish that it was found correct.