Answer:
Step-by-step explanation:
[tex]y = \dfrac{1}{2}*(x - 3)^{2}\\\\\\2y = (x-3)^{2}\\\\\\2y = x^{2}-2*x*3 + 3^{2}\\\\\\2y = x^{2} - 6x + 9 \ --------------(I)[/tex]
y = -x + 7 -------------(II)
Plugin y = -x + 7 in equation (I)
2(-x + 7) =x² - 6x + 9
-2x + 14 =x ² - 6x + 9
x² - 6x + 9 = -2x + 14
x² - 6x + 9 + 2x - 14 = 0
x² - 4x - 5 = 0
x² -5x + x - 5 = 0
x(x - 5) + 1(x - 5) = 0
(x -5)(x + 1) = 0
x- 5 = 0 ; x + 1 = 0
x = 5 ; x = -1
When x = 5 ⇒ y = -5 + 7 = 2
When x = -1 ⇒ y = -(-1) + 7 = 1 + 7 = 8
Solution (5 , 2) & (-1 , 8)
