Answer:
(4, 3 ) and (1.5, 8 )
Step-by-step explanation:
Given the 2 equations
2x + y = 11 → (1)
xy = 12 → (2)
Rearrange (1) expressing y in terms of x by subtracting 2x from both sides.
y = 11 - 2x → (3)
Substitute y = 11 - 2x into (2
x(11 - 2x) = 12 , that is
11x - 2x² = 12 ( subtract 12 from both sides )
11x - 2x² - 12 = 0
2x² - 11x + 12 = 0 ← in standard form
(x - 4)(2x - 3) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 4 = 0 ⇒ x = 4
2x - 3 = 0 ⇒ 2x = 3 ⇒ x = 1.5
Substitute these values into (3) for corresponding values of y
x = 4 : y = 11 - 2(4) = 11 - 8 = 3 ⇒ (4, 3 )
x = 1.5 : y = 11 - 2(1.5) = 11 - 3 = 8 ⇒ (1.5, 8 )
