When the る - Verb 合（あ）わせる (sometimes 併（あ）せる) is seen in the form 合（あ）わせて, it conveys that something has been made to ‘match (A)’ or ‘fit with (A)’. (A) being a noun that appears before
に, followed by 合（あ）わせて. This structure can also have the nuance of ‘in accordance with (A)’, highlighting that (A) is the governing factor.
It is also possible to see the う - Verb
合（あ）う used in its past tense form, linking an (A) noun to a (B) noun. This has a similar meaning, but is closer to ‘(B) that has met (A)’.
In sentences that use either of these expressions, more information is usually given about why something is happening in accordance with (A), or what the purpose of (B) meeting (A) is/was.
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音楽（おんがく）に合（あ）わせてにギターを弾（ひ）く練習（れんしゅう）をしています。
I am practicing playing my guitar along with music.
相手（あいて）に合（あ）わせて話（はな）し方（かた）を変（か）えるのは疲（つ）れる。
It is exhausting to change how you talk in accordance with who you are talking to.
このソファーにあったテーブルを買（か）おう。
Lets buy a table that matches this couch.
壁紙（かべがみ）にあった家具（かぐ）が欲（ほ）しい。
I want furniture that matches the wallpaper.
With 合（あ）わせて, sometimes the meaning is as simple as ‘at the same time as (A)’, or ‘together with (A)’. However, (A) will still be perceived as being the primary cause/reason for whatever happens in the (B) part of the sentence.