Chapter 7 - Section 7.4 - Systems of Nonlinear Equations in Two Variables - Exercise Set - Page 850: 15

$(-1,2)$ or, $(4,-3)$

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