A dog-sitting company is trying to grow its business. It had 30 clients when they started its business and wants to increase by 5 new clients each week. Use an arithmetic sequence to write the number of clients the business will have in the first six weeks. Use the sequence to write a function to represent this real-world situation and determine the range of the function for the first four weeks of data.

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So the first thing we do is to multiply the top equation by 3. the reason i want to do this is i notice there will be a 6y on both equations and can possibly add/subtract them. so we get 6y = -3x + 27. adding that and the second equation we get 6x = 27-15 which is 12. divide by 6 and we get 2. ∴ x = 2. substituting 2 into the first equation we get 2y = -2 + 9 which is 7. divide by 2 and we get 7/2. ∴ y = 7/2, x = 2.