Chapter 6 - Systems of Equations and Inequalities - 6-6 Systems of Linear Inequalities - Practice and Problem-Solving Exercises - Page 400: 33

C) III

$y\leq-1.5x-2$ Test the origin (0,0) $y\leq-1.5x-2$ $0 \leq -1.5*0 -2$ $0 \leq -2$ (false) The origin is not part of the solution set, so either region III or IV is the solution area. $3y-9x\geq6$ Test the origin (0,0) $3y-9x\geq6$ $3*0 - 9*0 \geq 6$ $0-0 \geq 6$ $0 \geq 6$ (false) Only section II or III can be the area. Region III is the only region that fits both requirements.