Final answer:
The system of equations has an infinite number of solutions with the correct solution being y = x² - 6x (Option 1), as the equation y = x² - 6x directly assigns the value of x² - 6x to y.
Step-by-step explanation:
The solution to the system of equations consisting of x² - 6x = x² - 6x and y = x² - 6x can be analyzed by comparing both equations. The first equation simplifies to 0 = 0, which indicates that the first equation is true for all values of x. Thus, there is an infinite number of solutions to the first equation.
For the second equation, it assigns the value of x² - 6x to y directly. Therefore, the correct solution for the system of equations is y = x² - 6x, which is listed as Option 1: y = x² - 6x.