To write a system of linear equations based on the given graph, we need to identify the equations of each line by finding their slopes and y-intercepts.

Analysis of the Lines:

Line 1 (Steeper Line):

1. It passes through points like (0, 6) and (2, 0).
2. The slope $m$ is calculated as: $m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 6}{2 - 0} = -3$
3. The y-intercept $b$ is 6 (the point where the line crosses the y-axis).

Thus, the equation of Line 1 is: $y = -3x + 6$

Line 2 (Less Steep Line):

1. It passes through points like (0, -2) and (3, 3).
2. The slope $m$ is calculated as: $m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{3 - (-2)}{3 - 0} = \frac{5}{3}$
3. The y-intercept $b$ is -2.

Thus, the equation of Line 2 is: $y = \frac{5}{3}x - 2$

Final System of Equations:

The system of linear equations for the graph is: