thank you so much! we've been learning about how to solve these using matrices, but one mistake can upset the entire solution. for the first one, I thought I was doing everything correctly, but I got huge numbers. They actually worked for the first equation, and i'm not sure why they worked for the first and not for the other three... i'm not sure what I did wrong. It took me about 20 minutes just to do it all and I get so frustrated. Math is definitely not my specialty.