I was given a problem to solve this evening that seems to have lost my understanding.

What are the ordered triples of real numbers (x,y,z) that satisfy

(x+y)(x+y+z)=120

(y+z)(x+y+z)=96

(x+z)(x+y+z)=72

Now I have no idea how to complete this problem or how it would be done. Sadly, an in-depth explanation would be useful if possible.

Our educator said that there were two sets, and I was able to find one.

(4,6,2) and this value was achieved without well knowledge of what I was doing.