Chapter 13 - Section 13.3 - Solving Nonlinear Systems of Equations - Exercise Set - Page 948: 14

${(1,1), (-1/6, -6)}$

$6x-y=5$ $xy=1$ $6x-y=5$ $6x-y+y-5=5+y-5$ $6x-5=y$ $xy=1$ $x(6x-5)=1$ $6x^2-5x=1$ $6x^2-5x-1=1-1$ $6x^2-5x-1=0$ $(x-1)(6x+1)=0$ $x-1=0$ $x-1+1=0+1$ $x=1$ $6x+1=0$ $6x+1-1=0-1$ $6x=-1$ $6x/6=-1/6$ $x=-1/6$ $xy=1$ $x=1$ $xy=1$ $1*y=1$ $y=1$ $x=-1/6$ $xy=1$ $-1/6*y=1$ $-1/6*y*-6=1*-6$ $y=-6$