According to the meaning of the question: -b/a=2 ①
( 1/2){ab|=4 ②
b=-2a ③
a^2b^2=64 ④
b^2=4a^2
4a^4=64
a^4= 16
a= 2
b= 4
So there are two groups of solutions: (a=2, b=-4) (a=-2, b=4).
So the linear equation is x/2-y/4= 1 2x-y-4=0.
x/(-2)+y/4= 1 2x-y+4=0