Answer:
(5, 10 ) and (10, - 5 )
Explanation:
x² + y² = 125 → (1)
3x + y = 25 ( subtract 3x from both sides )
y = 25 - 3x → (2)
substitute y = 25 - 3x into (1)
x² + (25 - 3x)² = 125 ← expand parenthesis using FOIL
x² + 625 - 150x + 9x² = 125
10x² - 150x + 625 = 125 ( subtract 125 from both sides )
10x² - 150x + 500 = 0 ( divide through by 10 )
x² - 15x + 50 = 0 ← in standard form
(x - 5)(x - 10) = 0 ← in factored form
equate each factor to zero and solve for x
x - 5 = 0 ⇒ x = 5
x - 10 = 0 ⇒ x = 10
substitute these values into (2) for corresponding values of y
x = 5 : y = 25 - 3(5) = 25 - 15 = 10 ⇒ (5, 10 )
x = 10 : y = 25 - 3(10) = 25 - 30 = - 5 ⇒ (10, - 5 )