Final answer:
To find the best approximate solutions for a system of inequalities, one plots known points, examines the graph for intersection areas satisfying both inequalities, and uses regression analysis where appropriate.
Step-by-step explanation:
The student's question pertains to finding the best approximate solutions for a system of inequalities from a given graph, with reference to function values f(x) and g(x). One common approach to this task is to use graphical methods to solve the problems.
As noted, data taken from graphs are assumed to be accurate to three digits, which allows for some precision in the analysis. To address this question effectively, a table of known points would need to be plotted on a graph and the dependence of y on x observed to determine the area of intersection that satisfies both inequalities.
In the absence of the specific graph in question, it's necessary to extrapolate from the information provided. Given the function f(x) is described as a horizontal line and is restricted to the domain 0 ≤ x ≤ 20, we would look for the range of x-values that fall under both f(x) and g(x), based on the graph's depiction.
As for least-squares line, this indicates the use of regression analysis to find a line that best fits the data, which in turn helps identify possible outliers or if a linear model is suitable.