Georgia is a farmer and wants to plant a crop of tomato plants so she can sell her crop at the local farmer's market. she already has a large number of plants cultivated from last year's harvest. each should produce an average of 35 tomatoes per plant during the growing season. she has found a nursery to buy more tomato plants at which are a different type. she found that these tomato plants will cost $5.25 each and should produce 25 tomatoes per plant on average over the course of the growing season. when planting, she wants to arrange the plants so that there are 5 fewer plants in each column than there are in each row. georgia can spend no more than $500 on the tomato plants. in order to meet customer demands, she needs to produce at least 5,000 tomatoes during the growing season. let x represent the number of plants in a row, and let y represent the number of plants that georgia already has.

create a system of inequalities to find the number of plants in a row and the number of plants georgia already has, and use it to determine how many of the solutions are viable.