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

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

Here, we have $x-y=1 \implies x=y+1$ Now, $(y+1)^2+y^2=25$ This gives: $y^2+y-12=0$ This yields : $(y+4) (y-3)=0$ when $y=-4$ then we have $x=-4+1=-3$ when $y=3$ then we have $x=3+1=4$ Hence, our answers are: $(-3,-4)$ or, $(4,3)$