One of the simplest illustrations of use of linear equations in real world situations could involve anticipating information regarding gasoline use while on vacation. Given a constant number of miles covered for each gallon of gas used by the vehicle and a constant price per gallon to purchase the gas, one can determine the number of miles to be traveled and figure out the cost of gasoline for the trip.
If you wanted to refine your estimate, you would figure different miles per gallon figures for the miles that would be highway speed as different from the miles that will be driven in city traffic. You could attempt to determine how the actual cost per gallon will vary from state to state due to taxes and figure different costs for different segments of your trip. By adding the different equations together, you could still figure your total expense.