Answer the following questions related to the system of linear inequalities x+y≤8 and 3x−y≥6. Assume x and y are real numbers.
a. (i) Define the term "feasible region" for a system of linear inequalities in two variables.
b. (ii) Without drawing the graphs, determine whether every point that satisfies both inequalities necessarily lies above, below, or on the line y=x. Give a brief justification.
c. (iii) Using suitable reasoning, state whether the feasible region of the given system is bounded or unbounded.