The type of sentence given is a compound sentence. It is a compound sentence because it consists of two independent sentences: "I already said yes to someone else" and "I can't go to the dance with you". In order to link the two sentences, the conjunction "because" is used.
Your answer would be that the sentence above is a complex sentence.
Explanation:
A complex sentence has one independent clause and at least one dependent clause. The difference between an independent clause and a dependent one is that the former can stand alone as a sentence because it represents a complete idea. On the contrary, dependent clauses are dependent on the independent part of the sentence in order to complete their meaning, so they fail to stand alone as sentences (see 1). In the sentence above, the dependent clause has been introduced by the subordinating conjunction <em>because.</em>
