Very good solutions came in from Christopher Kassam, age 13, Epsom; from Ian Green of Cooper's Coborn School; Lizzie and Sheli, Ruoyi Sun, Sarah Rogers, Arti Patel from the NLCS Puzzle Club; Alex Lam from St Peter's College, Adelaide; Beth Carroll, Sheila Luk, Alicia Maultby and Rachel Walker from the Mount School, York; Alex Filz from Ousedale School, Milton Keynes; Farhan Iskander, Foxford School, Coventry; and Christopher Dorrington and Lorn Tao, Stamford School. Well done all of you.
This is the solution from Lizzie and Sheli:
We realised that if you multiplied all the equations together and simplified it you ended up with:
The solutions are therefore$x= 3/2$, $y= 2/3$ and $z = 6$ or $x=-3/2$, $y= -2/3$ and $z = -6$ (where $x, y$ and $z$ all have the same sign).