Solve the system y = -x + 7 and y = -0.5(x - 3)^2 + 8.
Please explain your answer in two or more sentences.
(I will give 20 points)

(1,6) & (7,0)

Step-by-step explanation:

y = -x + 7

y = -0.5(x - 3)² + 8

To solve the system, solve these two equations simultaneously

-x + 7 = -0.5(x - 3)² + 8

-x + 7 = -0.5(x² - 6x + 9) + 8

-x + 7 = -0.5x² + 3x - 4.5 + 8

0.5x² - 4x + 3.5 = 0

x² - 8x + 7 = 0

x² - 7x - x + 7 = 0

x(x - 7) - (x - 7) = 0

(x - 1)(x - 7) = 0

x = 1, 7

y = -1 + 7 = 6

y = -7 + 7 = 0

(1,6) (7,0)

Since the system has two distinct solutions, the line and the curve meet at two distinct poibts9: (1,6) & (7,0)