Final answer:
The system of equations x² - 6x = x² - 6x does not determine a unique solution but rather an infinite number of solutions that lie along the parabola y = x² - 6x.
Step-by-step explanation:
The student has asked for the solution to the system of equations x² - 6x = x² - 6x. The given equations are identical, which means every x value will satisfy the equation. Since the two equations are the same, the system does not define a unique point of intersection, rather, every point on y = x² - 6x lies on the curve and is a solution to the system.
This could be viewed as an equation with infinite solutions where the graph of one equation is exactly atop the other. In other words, the system does not determine a single solution, but rather an infinite number of solutions that lie along the parabola defined by y = x² - 6x.
When solving quadratic equations like x² + bx + c = 0, we typically use the quadratic formula to find the values of x that satisfy the equation. However, since the two given equations are the same, there is no need to solve; the answer is the graph of the equation y = x² - 6x itself.