Question

X² - xy = 0
x + y = 1

Answer 1

(0, 1 ) and (
`(1)/(2)`,
`(1)/(2)` )

Explanation:

Given the 2 equations

x³ - xy = 0 → (1)

x + y = 1 → (2) ( subtract x from both sides )

y = 1 - x → (3)

Substitute y = 1 - x into (1)

x² - x(1 - x) = 0

x² - x + x² = 0

2x² - x = 0 ← factor out x from each term on the left side

x(2x - 1) = 0

Equate each factor to zero and solve for x

x = 0

2x - 1 = 0 ⇒ 2x = 1 ⇒ x =
`(1)/(2)`

Substitute these values into (3) for corresponding values of y

x = 0 : y = 1 - 0 = 1 ⇒ (0, 1 )

x =
`(1)/(2)` : y = 1 -
`(1)/(2)` =
`(1)/(2)` ⇒ (
`(1)/(2)`,
`(1)/(2)` )