Tom determines the system of equations below has two solutions, one of which is located at the vertex of the parabola. equation 1: (x - 3) 2 = y - 4 equation 2: y = - x bin order for this solution to be reasonable, which qualifications must be met?

(x - 3) ² = y - 4

y = (x - 3) ² + 4

One solution is located at the vertex: (3, 4).

y = - x + b

4 = - 3 + b

b = 7

(x - 3) ² = - x + 7 - 4

x² - 6 x + 9 = - x + 3

x² - 5 x + 6 = 0

x² - 2 x - 3 x + 6 = 0

x (x - 2) - 3 (x - 2) = 0

(x - 2) (x - 3) = 0

x 1 = 2, x 2 = 3

y 1 = 5, y 2 = 4.

In order for this solution to be reasonable, the 2nd equation must be:

y = - x + 7