Solve the following system of equations: y=6-x

y=x^2-6x+6

(0, 6) and (5, 1)

Step-by-step explanation:

Given the 2 equations

y = 6 - x → (1)

y = x² - 6x + 6 → (2)

Substitute y = x² - 6x + 6 into (1)

x² - 6x + 6 = 6 - x (subtract 6 - x from both sides)

x² - 5x = 0 ← factor out x from each term on the left side

x (x - 5) = 0

Equate each factor to zero and solve for x

x = 0

x - 5 = 0 ⇒ x = 5

Substitute these values into (1) for corresponding value of y

x = 0 : y = 6 - 0 = 6 ⇒ (0, 6)

x = 5 : y = 6 - 5 = 1 ⇒ (5, 1)