Answer:
(4, 2 ) and (2, 4 )
Explanation:
xy = 8 → (1)
y = - x + 6 → (2)
substitute y = - x + 6 into (1)
x(- x + 6) = 8
- x² + 6x = 8 ( subtract 8 from both sides )
- x² + 6x - 8 = 0 ( multiply through by - 1 )
x² - 6x + 8 = 0 ← in standard form
(x - 4)(x - 2) = 0 ← in factored form
equate each factor to zero and solve for x
x - 4 = 0 ⇒ x = 4
x - 2 = 0 ⇒ x = 2
substitute these values into (2) for corresponding values of y
x = 4 : y = - 4 + 6 = 2 ⇒ (4, 2 )
x = 2 : y = - 2 + 6 = 4 ⇒ (2, 4 )