Answer:
(2, 4 ) and (4, 2 )
Explanation:
y = 6 - x → (1)
x² + y² = 20 → (2)
substitute y = 6 - x into (2)
x² + (6 - x)² = 20 ← expand squared factor using FOIL
x² + 36 - 12x + x² = 20
2x² - 12x + 36 = 20 ( subtract 20 from both sides )
2x² - 12x + 16 = 0 ( divide through by 2 )
x² - 6x + 8 = 0 ← in standard form
(x - 2)(x - 4) = 0 ← in factored form
equate each factor to zero and solve for x
x - 2 = 0 ⇒ x = 2
x - 4 = 0 ⇒ x = 4
substitute these values into (1) for corresponding values of y
x = 2 : y = 6 - 2 = 4 ⇒ (2, 4 )
x = 4 : y = 6 - 4 = 2 ⇒ (4, 2 )