Answer
$(2,2)$, $(2,4)$
Work Step by Step
After using the addition method, we get
$2x^2-8x+8=0$
Re-arrange as: $x^2-4x+4=0$
This gives: $(x-2)^2=0$
when $x=2$ then we have $(2)^2-y^2-4(2)+6y-4=0 \implies y^2-6y+8=0$
This gives: $(y-2)(y-4)=0$
we have $y=2,4$
Hence, our answers are: $(2,2)$, $(2,4)$