Final answer:
To solve the system graphically, convert the inequalities to y = mx + b form, graph the lines, and shade the solution regions. The intersection of the shaded regions is the solution set for the system.
Step-by-step explanation:
To solve the system of linear inequalities graphically, we first need to convert each inequality into the form of y = mx + b, which represents a straight line on a graph. The given inequalities are 2x + 5y ≤ 20 and 2x - 5y ≥ -5. We will now find the y-intercept (b) and slope (m) of these lines.
For the first inequality, we rewrite it as 5y ≤ -2x + 20 and then y ≤ -2/5x + 4, which has a slope of -2/5 and a y-intercept of 4. For the second inequality, we rewrite it as 5y ≥ 2x + 5 and then y ≥ 2/5x + 1, which has a slope of 2/5 and a y-intercept of 1.
Next, we graph these two lines on the coordinate plane. The area below the line y = -2/5x + 4 represents the solutions for the first inequality, and the area above the line y = 2/5x + 1 represents the solutions for the second inequality. We will shade these areas respectively to represent all possible solutions to the system.
The intersection of these shaded areas represents the set of solutions that satisfy both inequalities simultaneously. Labeling the graph with f(x) and x and scaling the axes with the maximum values given, we can consider f(x) = 10 for 0≤x≤20, which is a horizontal line. This line is restricted between x = 0 and x = 20. In this context, f(x) is not directly relevant to the solution of the system of inequalities. However, knowing how to graph a simple function such as a constant can be helpful in understanding graphing concepts more broadly.