they drive me crazy

bruh for this one single question, I got an answer by transposing matrices, I got another answer by graphing + algebra, and the answer key got ANOTHER answer
I mean I don't think I can question the transposing method because I used my ti to do the calculations, but then I did the graphing method's calculations with my calculator (the problem has some disgusting numbers), and the answer key is answer key...although the answer key can trip

I hold full rights to believe that the existence of inequalities is to murder my braincells I've been working on this problem for almost an hour trying to verify my answers but my work is proven to be fruitless AHHHHHHHHHHH

thank you