Chapter 7 - Section 7.4 - Systems of Nonlinear Equations in Two Variables - Exercise Set - Page 850: 17

$(0,1)$ or, $(4,-3)$

Here, we have $y=1-x$ Now, $(x-1)^2+[(1-x)^2+2)^2=10$ This gives: $2x^2-8x=0$ This yields : $x(x-4)=0$ when $x=0$ then we have $y=1-0=1$ when $x=4$ then we have $y=1-4=-3$ Hence, our answers are: $(0,1)$ or, $(4,-3)$