Answer:
(4, 3 ) and (2.5, 3.5 )
Explanation:
Given the 2 equations
x + 3y = 13 → (1)
x² + 3y² = 43 → (2)
Rearrange (1) expressing x in terms of y, that is
x = 13 - 3y → (3)
Substitute x = 13 - 3y into (2)
(13 - 3y)² + 3y² = 43 ← expand factor using FOIL
169 - 78y + 9y² + 3y² = 43
12y² - 78y + 169 = 43 ( subtract 43 from both sides )
12y² - 78y + 126 = 0 ( divide through by 6 )
2y² - 13y + 21 = 0 ← in standard form
(y - 3)(2y - 7) = 0 ← in factored form
Equate each factor to zero and solve for y
y - 3 = 0 ⇒ y = 3
2y - 7 = 0 ⇒ 2y = 7 ⇒ y = 3.5
Substitute these values into (3) for corresponding values of x
y = 3 → x = 13 - 3(3) = 13 - 9 = 4 ⇒ (4, 3 )
y = 3.5 → x = 13 - 3(3.5) = 13 - 10.5 = 2.5 ⇒ (2.5, 3.5 )