"I will cook with my friend on the weekends."
Wouldn't 週まつ、友だちといっしょにりょうりします be more accurate? Is there any difference in the nuance
The range of pulldown is wrong. It should be not 'とり' but 'と'. 'り' is the first letter of 'りょうり(料理)'. I think that 'と' is translated as 'with'. 'With' has some translated ways '〜と', '〜と一緒に' etc.
http://ejje.weblio.jp/content/with （with 主な意味：main meaning）
I don't know which is best. But I think your translation should be accepted.
I feel, without いっしょに, is that you and your friend are cooking, but not necessarily at the same time in the same place.
For whoever needs it, the romaji is: "Shuumatsu, tomodachi to ryouri shimasu." Shuu: week -matsu: end Tomo: friend -dachi: (pluralizer for people) To: with Ryouri: to cook/cooking *Shimasu: will do/ to do
I'm not native, but i think my translations are just about correct, if not, someone please corrrect me. <3