Employees of a venue are setting up for a wedding in a hall that has indoor and patio seating. They are trying to decide how to best arrange the flowers. The bride instructed the employees that she wants some of the aisles to have bouquets of only roses and some of the aisles to have bouquets of only dahlias.

For the indoor area, they have decided that in each rose-only aisle, there will be 4 less bouquets of roses than there are roses in each bouquet. There will be 6 rose aisles and one aisle with 2 bouquets of dahlias.

The patio seating area will have one aisle with 4 bouquets of roses and one aisle with 8 bouquets of dahlias.

They plan on using 100 total flowers for the indoor aisles and 132 total flowers for the patio aisles. They want to apply these numbers to determine how many flowers will go in the bouquets if all of the bouquets have an equal number of flowers.

Create a system of equations to model the situation, and use it to determine how many of the solutions are viable.