Answer:
(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 )
