Answer:
(1, 2 ), (2, 1 )
Step-by-step explanation:
Given the 2 equations
x + y = 3 → (1)
x² + y² = 5 → (2)
Rearrange (1) expressing y in terms of x by subtracting x from both sides
y = 3 - x → (3)
Substitute y = 3 - x into (2)
x² + (3 - x)² = 5 ← expand and simplify left side
x² + 9 - 6x + x² = 5
2x² - 6x + 9 = 5 ( subtract 5 from both sides )
2x² - 6x + 4 ( divide through by 2 )
x² - 3x + 2 = 0 ← in standard form
(x - 1)(x - 2) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 1 = 0 ⇒ x = 1
x - 2 = 0 ⇒ x = 2
Substitute these values into (3) for corresponding values of y
x = 1 : y = 3 - 1 = 2 ⇒ (1, 2 )
x = 2 : y = 3 - 2 = 1 ⇒ (2, 1 )
