[tex]x=2y-2[/tex]
[tex]xy=84[/tex]
Plug the first equation into the second to get
[tex](2y-2)y=2y^2-2y=84\implies 2y^2-2y-84=0\implies y^2-y-42=(y-7)(y+6)=0[/tex]
It's clear that both integers are positive, so it must be the case that [tex]y=7[/tex], which means [tex]x=12[/tex].
