solve simultaneous equation,*
*4m=(9-n)²*
*4n=(3-m)²*
Show workings
multiply the 2nd equation by 4^2=16 and you have
64n=(12-4m)²
64n=(12-(9-n)²)²
Now just expand that out and solve the 4th-degree equation for n. Then you can get m.
Sorry, it has no rational roots, so you'll have to use numeric or graphical methods.