Chapter 5, Systems of Equations and Inequalities - Section 5.4 - Systems of Nonlinear Equations - 5.4 Exercises - Page 466: 23

$(6,2)$ and $(-2,-6)$

Step 1. Rewrite the equations. $y=x-4$ $xy=12$ Step 2. Substitute the first equation to the second one and solve for $x$. $x(x-4)=12$ $x^2-4x=12$ $x^2-4x-12=0$ $(x-6)(x+2)=0$ $x=6$ and $x=-2$ Step 3. Solve for $y$. For $x=6$, $y=6-4=2$ For $x=-2$, $y=-2-4=-6$ Step 4. Conclude the solutions. The solutions are $(6,2)$ and $(-2,-6)$.