Final Answer:
The solution to the given system of equations is a single point, indicating that the two lines intersect at a unique solution.
Step-by-step explanation:
The system of equations provided, 12y = 9x + 33 and 20y = 15x + 55, can be analyzed to determine the nature of the solution. These equations represent two linear functions in the form y = mx + b, where m is the slope and b is the y-intercept.
When comparing the coefficients of x and y in both equations, it becomes evident that the slopes (9/12 and 15/20) are equal. Moreover, the y-intercepts (33 and 55) are also different. These characteristics indicate that the two lines represented by these equations are parallel.
Since parallel lines never intersect, the conclusion is that the system of equations has no solution. However, if the coefficients of x and y were the same in both equations, it would imply that the lines are identical, resulting in infinitely many solutions. In this case, the distinct slopes confirm a lack of intersection, leading to no common solution for the given system of equations.