Answer
See below
Work Step by Step
Given: $y^2-x^2+2x-5=0\\x^2+y^2-2x-3=0$
Add it together: $2y^2-8=0\\2(y^2-4)=0\\y=\pm 2$
Find x: $x^2+4-2x-3=0\\x^2-2x+1=0\\(x-1)^2=0\\x=1$
Test: $1^2+4-2(1)-3=0$
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