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x<0
y>0
2x+4y-k²+k-2=0
x-2y+k+3=0 |∙2
2x+4y-k²+k-2=0
2x-4y+2k+6=0
______________+
4x-k²+3k+4=0
x=1/4k²-3/4k-1<0
k²-3k-4<0
Δ=9+16=25
k1=(3-5)/2=-1
k1=(3+5)/2=4
k∈(-1,4)
2(1/4k²-3/4k-1)+4y-k²+k-2=0
1/2k² -3/2k -2+4y-k²+k-2=0
-1/2 k² -1/2 k -4 = -4y
y= 1/8 k² +1/8k +1>0
1k² +1k +8>0
Δ=1-32<0
k∈R
k∈(-1,4)