Chapter 7 - Section 7.4 - Systems of Nonlinear Equations in Two Variables - Exercise Set - Page 850: 8

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

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