Answer :
xy=6
x=6/y......1
3x+2y=12
from1
3*(6/y)+2y=12
{after solving}2y^2-12y+18=0
y^2-6y+9=0 {taking y common}
y^2-3y-3y+9=0
y(y-3)-3(y-3)=0
y=3,3............2
putting 2 in 1
x=2.........3
9x^2+4y^2=
from 2 and 3
9*4+4*9=36+36=72
x=6/y......1
3x+2y=12
from1
3*(6/y)+2y=12
{after solving}2y^2-12y+18=0
y^2-6y+9=0 {taking y common}
y^2-3y-3y+9=0
y(y-3)-3(y-3)=0
y=3,3............2
putting 2 in 1
x=2.........3
9x^2+4y^2=
from 2 and 3
9*4+4*9=36+36=72
[tex]3x+2y=12\\
(3x+2y)^2=144\\
9x^2+12xy+4y^2=144\\\\
9x^2+4y^2=144-12xy\\
9x^2+4y^2=144-12\cdot6\\
9x^2+4y^2=144-72\\
\boxed{9x^2+4y^2=72}
[/tex]