Y-3=x

x^2-6x+13=y

A. (-5, 2)

B. (-2, 1)

C. (2, 5)

D. (8, 5)

y - 3 = x

x^2 - 6x + 13 = y

--

y = x + 3

x^2 - 6x + 13 = x + 3

x^2 - 7x + 10 = 0

x^2 - 5x - 2x + 10 = 0

x (x - 5) - 2 (x - 5) = 0

(x - 2) (x - 5) = 0

x = 2, or x = 5

The answers choices only have one solution where x = 2 or x = 5, so the answer is (2, 5).