x2-xy+3y2+2x-5y-4=0, x+2y=4.
Substitute x=4-2y in the first equation:
16-16y+4y2-4y+2y2+3y2+8-4y-5y-4=9y2-29y+20=0=(9y-20)(y-1).
Therefore y=20/9 or 1, making x=4-40/9=-4/9 or 2.
x2-y2=16/81-400/81=-384/81=-128/27; or 4-1=3.
(x,y)=(-4/9,20/9) or (2,1).