没关系，不要紧

The phrase '没关系 (méiguānxì)' is composed of '没 (méi)' meaning 'not' or 'without', and '关系 (guānxì)' meaning 'relation' or 'connection'. Together, it literally means 'no relation' or 'no connection', implying that something does not matter or is of no concern. Its usage as 'it's alright' or 'it doesn't matter' developed from this basic meaning. The phrase '不要紧 (bùyàojǐn)' is formed from '不 (bù)' meaning 'not', and '要紧 (yàojǐn)' meaning 'important' or 'serious'. Therefore, '不要紧' literally means 'not important' or 'not serious'. It is used to convey that something is not grave or does not warrant worry. Both phrases are commonly used in modern Mandarin Chinese to reassure someone that a situation is not serious, to dismiss an apology, or to indicate that something is not a problem. They are often used together, as in the user's query '没关系，不要紧', to emphasize the reassuring sentiment. The combination reinforces the idea that there is no need to worry and that the matter is not serious.