1. The problem asks us to find which ordered pairs satisfy the system of inequalities defined by the lines $y=2x$ and $y=-2x$ with the shaded region being the left half-plane $x \leq 0$. 2. The system can be interpreted as points $(x,y)$ that lie between the lines $y=2x$ and $y=-2x$ and also satisfy $x \leq 0$. 3. To check each point, we verify: - If $x \leq 0$ (point is in the left half-plane). - If $y$ lies between $-2x$ and $2x$ (inclusive). 4. Check each point: - $(0,0)$: $x=0 \leq 0$ true; $-2(0) = 0 \leq 0 \leq 2(0) = 0$ true; so $(0,0)$ is a solution. - $(2,2)$: $x=2 \leq 0$ false; discard. - $(-1,1)$: $x=-1 \leq 0$ true; check $-2(-1)=2 \leq 1 \leq 2(-1)=-2$ false (1 is not between 2 and -2); discard. - $(1,0)$: $x=1 \leq 0$ false; discard. - $(-2,2)$: $x=-2 \leq 0$ true; check $-2(-2)=4 \leq 2 \leq 2(-2)=-4$ false; discard. 5. Only $(0,0)$ satisfies the system. Final answer: $(0,0)$