![]() ![]() The lines cross because the price of rental per movie is different for the two options in the problem In this case, the slopes of the lines represent the price of a rental per movie. In other words, the lines are not parallel Remember that for a consistent system, the lines that make up the system intersect at single point. This example shows a real situation where a consistent system of equations is useful in finding a solution. You would have to rent 30 movies per year before the membership becomes the better option. Substitute the second equation into the first one: Since each equation is already solved for, we can easily solve the system with substitution. Now we need to find the exact intersection point. For the membership option the rental fee is, since you would pay $2 for each movie you rented įor the no membership option the rental fee is, since you would pay $3.50 for each movie you rented. The flat fee is the dollar amount you pay per year and the rental fee is the dollar amount you pay when you rent a movie. We'll call the number of movies you rent and the total cost of renting movies for a year. The choices are "membership" and "no membership". Since there are two different options to consider, we can write two different equations and form a system. Let's translate this problem into algebra. Rent before the membership becomes the cheaper option? Customers can pay a yearly membership of $45 and then rent each movie for $2 or they can choose not to pay the membership fee and rent each movie for $3.50. The movie rental store CineStar offers customers two choices. Real-World Application: Yearly Membership ![]()
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