Teachers, save “Company Profit VS Revenue” to assign it to your class.

A start-up company has invented a brand wireless headphone that they hope will compete with AirPods. They paid $450 in fees and production costs when they began the company, but now only have to pay $10 a month to continuously renew their patent on the product. This scenario is represented by the equation, y = 10x + 450. Each Month, the company makes on average $100. This is represented by y = 100x. Obviously, when the company began, they had to spend a large amount of money to get the company off the ground, but as time goes on, they hope to make back the money they spent and then some. Using the graph provided, please solve the system and determine after how many months (x) the company will have spent as much money as they made. In the description, please tell me your answer, and explain how you know this is the answer.