I would say your answers are not wrong, but I think they could be worded better. I put my suggestions in upper case:
(1) "NOSOTROS vamos a estudiar juntos."
This could also be worded in the feminine as "NOSOTRAS vamos a estudiar JUNTAS." In Spanish, there may be different masculine and feminine words.
(2) "YO voy a estudiar para sacar buenas notas."
Note my suggested changes were minor, i.e. adding "nosotros" or "nosotras" and a possible feminine "juntas" in (1), and adding "yo" for I in (2).
But I think it goes too far to say your answer is wrong. I think it could just be worded better.
By the way, thank you for posting your attempted answer along with your question. It is good to see the student tried to answer the question before asking for help. I wish more students would try that.