A small coffee shop mixes two blends, A and B, to create a 50-pound blend. Blend A costs \$6 per pound and blend B costs \(10 per pound. The final 50-pound blend has an average cost of \)8 per pound. Create a system of linear equations to represent this situation and then solve the system. Also, classify the system as: consistent independent, dependent, and/or inconsistent.

No solution because the average cost cannot be achieved by any combination of the two blends; therefore the system is inconsistent.

x = 20, y = 30; consistent and dependent because the cost equation must be a multiple of the quantity equation for feasibility.

Infinitely many solutions because the equations are multiples of each other when scaled to the average cost per pound, indicating that the two original equations are coincident.

x = 25, y = 25; consistent and independent, with one unique solution.