Steps to Solve

1. Identify the inequalities from the graph Examine the lines on the graph. Identify the boundaries of the shaded regions, which typically represent inequalities. The two lines appear to be:

   • One line sloping downwards, indicating a 'less than' inequality.
   • Another line sloping upwards, indicating a 'greater than' inequality.

2. Find the equations of the lines For each boundary line, determine the slope and the y-intercept to write the equations.

   • The downward sloping line crosses the y-axis around (0, 9) and travels through (2, 7). Use these points to find the slope: $$ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{7 - 9}{2 - 0} = -1 $$ The equation can be written as: $$ y \leq -x + 9 $$
   • The upward sloping line crosses the y-axis at approximately (0, -3) and through (5, 2). The slope is calculated as: $$ m = \frac{2 - (-3)}{5 - 0} = 1 $$ The equation is: $$ y \geq x - 3 $$

3. Combine the inequalities With both inequalities derived from their respective lines, express the system of inequalities: $$ \begin{cases} y \leq -x + 9 \ y \geq x - 3 \end{cases} $$

4. Determine the solution region The solution to this system is the area where the shaded regions overlap. This means you want to find points $(x, y)$ that satisfy both inequalities.