Chapter 7 - Section 7.4 - Systems of Nonlinear Equations in Two Variables - Exercise Set - Page 850: 12

$(-1,3)$ or, $(3, -5)$

Here, we have $y=-2x+1$ Now, $x^2+(-2x+1)^2=4$ This gives: $x^2-2x-3=0$ This yields : $(x+1)(x-3)=0$ when $x=-1$ then we have $y=-2(-1)+1=3$ when $x=3$ then we have $y=-2(3)+1=-5$ Hence, our answers are: $(-1,3)$ or, $(3, -5)$