Tom N. answered • 05/24/19
Strong proficiency in elementary and advanced mathematics
The best way to solve this set of equations is to go to the second one which is x2 -2x -3y +1 =0 and notice that the x2 -2x +1 combine to give (x-1)2 and the equation becomes (x-1)2 -3y = 0 or (x-1)2 = 3y. Use this in the first equation and expand the (y-3)2 term to give y2 -6y +9 and add the 3y to it to give y2 -6y +9 +3y = 9 which now becomes y2 -3y = 0 and y=0,3. For y=0 (x-1)2 =3•0 = 0 and x=1. So one set of points is (1,0). Now let y=3 to give (x-1)2 =3•3 =9 or x2 -2x +1 -8= 0 and x2 -2x -8 = 0 which factors to (x-4)(x+2) =0 or x=4,-2. So the other two sets of points are (-2,3) and (4,3) making b. the answer.
