1. Solve the system of equations below both algebraically and by graphing. Be sure to show all of your work and state your solution as an ordered pair.
2. The population of a country is initially 2.5 million people and is increasing by 0.8 million people every year. The country’s annual food supply is initially adequate for 4 million people and is increasing at a constant rate for an additional 0.4 million people per year.
a. Based on these assumptions, in approximately how many years will the country first experience shortages of food?
b. If the country doubled its initial food supply and maintained a constant rate of increase in the supply adequate for an additional 0.5 million people per year, would shortages still occur? If so, how many years would it take for shortages to occur? If not, explain.
c. If the country doubled the rate at which its food supply increases, in addition to doubling its initial food supply, would shortages still occur? If so, how many years would it take for shortages to occur? If not, explain.
3. Springfield will be opening a new high school in the fall. The number of underclassmen (9th and 10th graders) must fall between 500 and 600 (inclusive), the number of upperclassmen (11th and 12th graders) must fall between 400 and 500 (inclusive), and the number of students cannot exceed 1000.
a. Let x represent the number of underclassmen and y represent the number of upperclassmen. Write a system of inequalities that models the situation.
b. Graph the solution to the system of inequalities in part a.