The problem asks to determine which system of equations corresponds to the graph provided. Let's analyze it step-by-step.

1. Identifying the lines: The graph shows two intersecting lines. Let's find the equations for each line by examining their slopes and y-intercepts.

   • First line: It passes through points $(0, 2)$ and $(3, 0)$. The slope $m$ is given by: $m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 2}{3 - 0} = -\frac{2}{3}$ The equation of the line in slope-intercept form $y = mx + b$ is: $y = -\frac{2}{3}x + 2$ Multiply by 3 to eliminate the fraction: $3y = -2x + 6 \quad \text{or} \quad 2x + 3y = 6$

   • Second line: It passes through points $(0, -2)$ and $(6, 0)$. The slope $m$ is: $m = \frac{0 - (-2)}{6 - 0} = \frac{2}{6} = \frac{1}{3}$ The equation of this line is: $y = \frac{1}{3}x - 2$ Multiply by 3 to eliminate the fraction: $3y = x - 6 \quad \text{or} \quad x - 3y = 6$

2. Matching with given options: We now compare the simplified forms of the equations:

   • First line: $2x + 3y = 6$
   • Second line: $x - 3y = 6$

   None of the equations in the answer choices are presented exactly like this, but they could be manipulated. Looking at the choices closely, let's check option D:

   • $x + y = -2$ (manipulate $x - 3y = 6$) might correspond to a transformation in slope direction.