Lets Solve A Polynomial System

[@iMíccoli]

Kind of a boring one. x²-y²+2x-2y-(x-y)=0 (x+y)(x-y)+2(x-y)-(x-y)=0 (x-y)(x+y+2-1)=0 (x-y)(x+y+1)=0 First case x=y x²+3x-4=0 ==> (x-1)(x+4) so x=y=1 or x=y=-4 Second case x+y=-1 x²+x-1=4 x²+x-5=0 ∆=21 so x=[(√21)-1]/2 and y=[-(√21)-1]/2 or the opposite.

[@Qermaq]

I solved it from the thumbnail by manipulating (2) into a quadratic in y, quadratic formula and subbing my expression for y into (1), then manipulating that into a quartic in x. Used a familiar trick to find one root, used RRT to find another, then I found the weird ones. A bit of a slog, but I wonder what wizardry you will show us that I wish I knew before!

[@Qermaq]

1:39 HEY! That's the quartic I said was not hard to solve. Oh jeez....