Question

X+y=5_______(1) and x²-2y²=1 _______(2) solve for X And Y simultaneously​

Answer 1

Answer:

(3, 2 ) and (17, - 12 )

Step-by-step explanation:

Given the 2 equations

x + y = 5 → (1)

x² - 2y² = 1 → (2)

Rearrange (1) expressing y in terms of x by subtracting x from both sides

y = 5 - x → (3)

Substitute y = 5 - x into (2)

x² - 2(5 - x)² = 1 ← expand and simplify left side

x² - 2(25 - 10x + x²) = 1

x² - 50 + 20x - 2x² = 1

- x² + 20x - 50 = 1 ( subtract 1 from both sides )

- x² + 20x - 51 = 0 ← multiply through by - 1

x² - 20x + 51 = 0 ← in standard form

(x - 17)(x - 3) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 17 = 0 ⇒ x = 17

x - 3 = 0 ⇒ x = 3

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

x = 17 : y = 5 - 17 = - 12 ⇒ (17, - 12 )

x = 3 : y = 5 - 3 = 2 ⇒ (3, 2 )

Solutions are (3, 2 ) and (17, - 12 )