1. **State the problem:** We need to find which ordered pairs satisfy the system of inequalities represented by the two lines and their shading. 2. **Identify the lines and inequalities:** - The first line is solid, descending, passing through points (0,2) and (-2,6). The slope $m$ is calculated as: $$m=\frac{6-2}{-2-0}=\frac{4}{-2}=-2$$ The equation of the line using point-slope form with point (0,2) is: $$y-2=-2(x-0)\implies y=-2x+2$$ Since the shading is on the upper left side, the inequality is: $$y \geq -2x + 2$$ - The second line is dashed, vertical at $x=2$, shading is on the right side, so the inequality is: $$x > 2$$ 3. **Determine the solution region:** The solution region is where both inequalities hold: $$\begin{cases} y \geq -2x + 2 \\ x > 2 \end{cases}$$ 4. **Check each ordered pair:** - (0,0): $x=0 \not> 2$ no - (3,1): $x=3 > 2$ yes; check $y \geq -2(3)+2= -6+2=-4$; $1 \geq -4$ yes - (-2,3): $x=-2 \not> 2$ no - (-4,3): $x=-4 \not> 2$ no - (4,-3): $x=4 > 2$ yes; check $y \geq -2(4)+2= -8+2=-6$; $-3 \geq -6$ yes 5. **Conclusion:** The ordered pairs that satisfy the system are (3,1) and (4,-3).