Final answer:
The values of x and y are 7 and -13, respectively, and the point (x, y) lies in the fourth quadrant.
Step-by-step explanation:
The question asks to find the values of x and y given that the ordered pairs (x-3,-6) and (4,x+y) are equal, and then determine the quadrant in which the point (x,y) lies. Since the ordered pairs are equal, their corresponding elements must be equal, therefore we have two equations: x - 3 = 4 and -6 = x + y. Solving the first equation, we get x = 7. Substituting x = 7 into the second equation, we get -6 = 7 + y, which simplifies to y = -13.
Now that we have found x = 7 and y = -13, we can determine the quadrant of the point (x, y). Since x is positive and y is negative, the point (7, -13) lies in the fourth quadrant.